[1] The Stacks Project. http://stacks.math.columbia.edu, 2014. (Cited on pages 94, 411, and 420.)

[2] N., Addington. and R., Thomas. Hodge theory and derived categories of cubic fourfolds. Duke Math. J., 163(10):1885–1927, 2014. (Cited on page 384.)

[3] A., Altman. and S., Kleiman. Compactifying the Picard scheme. II. Amer. J. Math., 101(1):10–41, 1979. (Cited on page 238.)Google Scholar

[4] K., Amerik. and M., Verbitsky. Morrison–Kawamata cone conjecture for hyperkähler manifolds. 2014. arXiv:1408.3892. (Cited on page 174.)Google Scholar

[5] S., Anan'in and M., Verbitsky. Any component of moduli of polarized hyperkähler manifolds is dense in its deformation space. 2010. arXiv:1008.2480. (Cited on page 324.)

[6] Y., André. Mumford–Tate groups of mixed Hodge structures and the theorem of the fixed part. Compositio Math., 82(1):1–24, 1992. (Cited on page 122.)Google Scholar

[7] Y., André. On the Shafarevich and Tate conjectures for hyper-Kähler varieties. Math. Ann., 305(2):205–248, 1996. (Cited on pages 54, 58, 77, 79, 85, 92, 404, and 408.)Google Scholar

[8] Y., André. Pour une théorie inconditionnelle des motifs. Inst. Hautes Études Sci. Publ. Math., 83:5–49, 1996. (Cited on pages 79 and 400.)Google Scholar

[9] M., Aprodu. Brill–Noether theory for curves on K3 surfaces. In Contemporary geometry and topology and related topics, pages 1–12. Cluj University Press, Cluj-Napoca, 2008. (Cited on page 183.)

[10] E., Arbarello, M., Cornalba, and P., Griffiths. Geometry of algebraic curves. Vol. II, vol. 268 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Heidelberg, 2011. With a contribution by J. Harris. (Cited on pages 283 and 285.)

[11] E., Arbarello, M., Cornalba, P., Griffiths, and J., Harris. Geometry of algebraic curves. Vol. I, vol. 267 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, New York, 1985. (Cited on pages 17 and 183.)

[12] E. Artal, Bartolo, H., Tokunaga, and D.-Q., Zhang. Miranda–Persson's problem on extremal elliptic K3 surfaces. Pacific J. Math., 202(1):37–72, 2002. (Cited on page 253.)Google Scholar

[13] M., Artebani, J., Hausen, and A., Laface. On Cox rings of K3 surfaces. Compositio Math., 146(4):964–998, 2010. (Cited on pages 170 and 174.)Google Scholar

[14] M., Artebani, A., Sarti, and S., Taki. K3 surfaces with non-symplectic automorphisms of prime order. Math. Z., 268(1-2):507–533, 2011. With an appendix by S. Kondō. (Cited on page 356.)Google Scholar

[15] E., Artin. Geometric algebra. Interscience Publishers, New York and London, 1957. (Cited on pages 59, 61, and 142.)

[16] M., Artin. Supersingular K3 surfaces. Ann. Sci. École Norm. Sup. (4), 7:543–567 (1975), 1974. (Cited on pages 11, 273, 395, 401, 402, 407, 408, 425, 434, 435, and 436.)Google Scholar

[17] M., Artin. Versal deformations and algebraic stacks. Invent. Math., 27:165–189, 1974. (Cited on pages 90 and 416.)Google Scholar

[18] M., Artin. Néron models. In Arithmetic geometry (Storrs, CT, 1984), pages 213–230. Springer-Verlag, New York, 1986. (Cited on page 232.)

[19] M., Artin and B., Mazur. Formal groups arising from algebraic varieties. Ann. Sci. École Norm. Sup. (4), 10(1):87–131, 1977. (Cited on pages 416, 432, and 433.)Google Scholar

[20] M., Artin and P., Swinnerton-Dyer. The Shafarevich–Tate conjecture for pencils of elliptic curves on K3 surfaces. Invent. Math., 20:249–266, 1973. (Cited on pages 249, 406, 407, and 425.)Google Scholar

[21] M., Asakura and S., Saito. Surfaces over a p-adic field with infinite torsion in the Chow group of 0-cycles. Algebra Number Theory, 1(2):163–181, 2007. (Cited on page 270.)Google Scholar

[22] K., Ascher, K., Dasaratha, A., Perry, and R., Zhou. Derived equivalences and rational points of twisted K3 surfaces. 2015. arXiv:1506.01374. (Cited on page 379.)

[23] A., Ash, D., Mumford, M., Rapoport, and Y.-S., Tai. Smooth compactifications of locally symmetric varieties. Cambridge Mathematical Library. Cambridge University Press, Cambridge, second edition, 2010.With the collaboration of Peter Scholze. (Cited on page 167.)

[24] P., Aspinwall and R., Kallosh. Fixing all moduli for M-theory on K3×K3. J. High Energy Phys., (10):001, 20 pp. (electronic), 2005. (Cited on page 386.)Google Scholar

[25] P., Aspinwall and D., Morrison. String theory on K3 surfaces. In Mirror symmetry, II, vol. 1 of AMS/IP Stud. Adv. Math., pages 703–716. Amer. Math. Soc., Providence, RI, 1997. (Cited on pages x and 314.)

[26] M., Atiyah. On analytic surfaces with double points. Proc. Roy. Soc. London. Ser. A, 247:237–244, 1958. (Cited on page xi.)Google Scholar

[27] M., Atiyah and F., Hirzebruch. Analytic cycles on complex manifolds. Topology, 1:25–45, 1962. (Cited on page 38.)Google Scholar

[28] L., Bădescu. Algebraic surfaces. Universitext. Springer-Verlag, New York, 2001. (Cited on pages 3, 8, 15, 29, 33, and 221.)

[29] W., Baily and A., Borel. Compactification of arithmetic quotients of bounded symmetric domains. Ann. Math. (2), 84:442–528, 1966. (Cited on pages 82 and 105.)Google Scholar

[30] A., Baragar. The ample cone for a K3 surface. Canad. J. Math., 63(3):481–499, 2011. (Cited on page 173.)

[31] A., Baragar and D., McKinnon. K3 surfaces, rational curves, and rational points. J. Number Theory, 130(7):1470–1479, 2010. (Cited on page 298.)

[32] P., Bardsley and R., Richardson. Étale slices for algebraic transformation groups in characteristic p. Proc. Lond. Math. Soc. (3), 51(2):295–317, 1985. (Cited on page 94.)

[33] W., Barth, K., Hulek, C., Peters, and A.Van de, Ven. Compact complex surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete. Springer-Verlag, Berlin, 2004. (Cited on pages x, 2, 3, 4, 7, 11, 15, 26, 142, 146, 149, 157, 158, 173, 219, 221, 224, 244, 285, 319, 320, 324, and 351.)

[34] C., Bartocci, U., Bruzzo, and D. Hernández, Ruipérez. Fourier–Mukai and Nahm transforms in geometry and mathematical physics, vol. 276 of Progr. Math. Birkhäuser, Boston, 2009. (Cited on page 358.)

[35] H., Bass. Algebraic K-theory. W. A., Benjamin, New York and Amsterdam, 1968. (Cited on page 261.)

[36] V., Batyrev. Birational Calabi–Yau n-folds have equal Betti numbers. In New trends in algebraic geometry (Warwick, 1996), vol. 264 of Lond. Math. Soc. Lecture Note Ser., pages 1–11. Cambridge University Press, Cambridge, 1999. (Cited on page 294.)

[37] T., Bauer. Seshadri constants on algebraic surfaces. Math. Ann., 313(3):547–583, 1999. (Cited on page 168.)Google Scholar

[38] T., Bauer, S. Di, Rocco, and T., Szemberg. Generation of jets on K3 surfaces. J. Pure Appl. Algebra, 146(1):17–27, 2000. (Cited on page 33.)Google Scholar

[39] T., Bauer and M., Funke. Weyl and Zariski chambers on K3 surfaces. Forum Math., 24(3):609–625, 2012. (Cited on page 174.)Google Scholar

[40] A., Bayer and T., Bridgeland. Derived automorphism groups of K3 surfaces of Picard rank 1. 2013. arXiv:1310.8266. (Cited on page 376.)

[41] A., Bayer and E., Macrì. MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations. Invent. Math., 198(3):505–590, 2014. (Cited on page 218.)Google Scholar

[42] A., Bayer and E., Macrì. Projectivity and birational geometry of Bridgeland moduli spaces. J. Amer. Math. Soc., 27(3):707–752, 2014. (Cited on page 218.)Google Scholar

[43] A., Beauville. Surfaces algébriques complexes, vol. 54 of Astérisque. Soc. Math. France, Paris, 1978. (Cited on pages 3, 15, 18, 21, and 32.)

[44] A., Beauville. Sur le nombre maximum de points doubles d'une surface dans P3 (μ(5)= 31). In Journées de Géometrie Algébrique d'Angers, Juillet 1979, pages 207–215. Sijthoff & Noordhoff, Alphen aan den Rijn, 1980. (Cited on page 321.)Google Scholar

[45] A., Beauville. Variétés Kähleriennes dont la première classe de Chern est nulle. J. Differential Geom., 18(4):755–782 (1984), 1983. (Cited on page 216.)Google Scholar

[46] A., Beauville. Counting rational curves on K3 surfaces. Duke Math. J., 97(1):99–108, 1999. (Cited on page 294.)Google Scholar

[47] A., Beauville. Some stable vector bundles with reducible theta divisor. Manuscripta Math., 110(3):343–349, 2003. (Cited on page 187.)Google Scholar

[48] A., Beauville. Fano threefolds and K3 surfaces. In The Fano Conference, pages 175–184. University of Torino, Turin, 2004. (Cited on pages 99 and 279.)

[49] A., Beauville. La conjecture de Green générique [d'après C.|Voisin], Séminaire Bourbaki, Exposé 924, 2003/2004. Astérisque, 299:1–14, 2005. (Cited on pages x and 184.)Google Scholar

[50] A., Beauville. On the splitting of the Bloch–Beilinson filtration. In Algebraic cycles and motives. Vol. 2, vol. 344 of Lond. Math. Soc. Lecture Note Ser., pages 38–53. Cambridge University Press, Cambridge, 2007. (Cited on page 271.)

[51] A., Beauville. Antisymplectic involutions of holomorphic symplectic manifolds. J. Topol., 4(2):300–304, 2011. (Cited on page 357.)Google Scholar

[52] A., Beauville and R., Donagi. La variété des droites d'une hypersurface cubique de dimension 4. C. R. Acad. Sci. Paris Sér. I Math., 301(14):703–706, 1985. (Cited on page 14.)Google Scholar

[53] A., Beauville and C., Voisin. On the Chow ring of a K3 surface. J. Algebraic Geom., 13(3):417–426, 2004. (Cited on pages 268 and 269.)Google Scholar

[54] A., Beauville et al. Géométrie des surfaces K3: modules et périodes, vol. 126 of Astérisque. Soc. Math. France, Paris, 1985. (Cited on pages x, 15, 28, 47, 106, 114, 130, 131, 134, 138, 146, 147, 172, 173, 319, 320, 324, and 337.)

[55] K., Behrend, B., Conrad, D., Edidin, W., Fulton, B., Fantechi, L., Göttsche, and A., Kresch. Introduction to stacks. In progress. (Cited on pages 95, 96, and 97.)

[56] A., Beılinson. Higher regulators and values of L-functions. In Current problems in mathematics, Vol. 24, Itogi Nauki i Tekhniki, pages 181–238. Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1984. (Cited on page 261.)

[57] S., Belcastro. Picard lattices of families of K3 surfaces. ProQuest LLC, Ann Arbor, MI, 1997. PhD thesis, University of Michigan. (Cited on page 253.)

[58] O., Benoist. Construction de courbes sur les surfaces K3 [d'après Bogomolov–Hassett– Tschinkel, Charles, Li–Liedtke, Madapusi Pera, Maulik…], Séminaire Bourbaki, Exposé 1081, 2013–2014. 2014. (Cited on pages 99, 297, 407, and 436.)

[59] N., Bergeron, Z., Li, J., Millson, and C., Moeglin. The Noether–Lefschetz conjecture and generalizations. 2014. arXiv:1412.3774. (Cited on page 127.)

[60] J., Bertin, J.-P., Demailly, L., Illusie, and C., Peters. Introduction to Hodge theory, vol. 8 of SMF/AMS Texts and Monographs. Amer. Math. Soc., Providence, RI, 2002. (Cited on pages 106, 108, and 329.)

[61] A., Besse. Einstein manifolds. Classics in Mathematics. Springer-Verlag, Berlin, 2008. (Cited on page 338.)

[62] G., Bini. On automorphisms of some K3 surfaces with Picard number two. MCFA Annals, 4:1–3, 2007. (Cited on page 343.)

[63] G., Bini and A., Garbagnati. Quotients of the Dwork pencil. J. Geom. Phys., 75:173–198, 2014. (Cited on page 389.)Google Scholar

[64] C., Birkenhake and H., Lange. Complex tori, vol. 177 of Progr. Math. Birkhäuser, Boston 1999. (Cited on pages 10 and 58.)

[65] C., Birkenhake and H., Lange. Complex abelian varieties, vol. 302 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, second edition, 2004. (Cited on page 58.)

[66] S., Bloch. Torsion algebraic cycles and a theorem of Roitman. Compositio Math., 39(1):107–127, 1979. (Cited on page 256.)Google Scholar

[67] S., Bloch. Lectures on algebraic cycles. Duke University Mathematics Series, IV. Duke University Mathematics Department, Durham, NC, 1980. (Cited on pages 256, 260, 263, 264, and 271.)

[68] S., Bloch. Algebraic cycles and values of L-functions. J. Reine Angew. Math., 350:94–108, 1984. (Cited on page 261.)Google Scholar

[69] F., Bogomolov, B., Hassett, and Y., Tschinkel. Constructing rational curves on K3 surfaces. Duke Math. J., 157(3):535–550, 2011. (Cited on pages 272, 273, 274, 277, 278, 281, 285, 286, 287, 289, 291, and 292.)Google Scholar

[70] F., Bogomolov and Y., Tschinkel. Density of rational points on elliptic K3 surfaces. Asian J. Math., 4(2):351–368, 2000. (Cited on pages 281 and 298.)Google Scholar

[71] F., Bogomolov and Y., Tschinkel. Rational curves and points on K3 surfaces. Amer. J. Math., 127(4):825–835, 2005. (Cited on pages 274, 282, and 329.)Google Scholar

[72] S., Boissière, M., Nieper-Wißkirchen, and A., Sarti. Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties. J. Math. Pures Appl. (9), 95(5): 553–563, 2011. (Cited on page 357.)Google Scholar

[73] S., Boissière and A., Sarti. Counting lines on surfaces. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 6(1):39–52, 2007. (Cited on page 297.)Google Scholar

[74] S., Boissière and A., Sarti. On the Néron–Severi group of surfaces with many lines. Proc. Amer. Math. Soc., 136(11):3861–3867, 2008. (Cited on page 390.)Google Scholar

[75] C., Borcea. Diffeomorphisms of a K3 surface. Math. Ann., 275(1):1–4, 1986. (Cited on page 143.)Google Scholar

[76] C., Borcea. K3 surfaces and complex multiplication. Rev. Roumaine Math. Pures Appl., 31(6):499–505, 1986. (Cited on page 52.)Google Scholar

[77] R., Borcherds. Coxeter groups, Lorentzian lattices, and K3 surfaces. Internat. Math. Res. Notices, 19:1011–1031, 1998. (Cited on pages 326, 327, 329, 341, and 357.)Google Scholar

[78] R., Borcherds, L., Katzarkov, T., Pantev, and N., Shepherd-Barron. Families of K3 surfaces. J. Algebraic Geom., 7(1):183–193, 1998. (Cited on page 111.)Google Scholar

[79] A., Borel. Some metric properties of arithmetic quotients of symmetric spaces and an extension theorem. J. Differential Geometry, 6:543–560, 1972. Collection of articles dedicated to S. S., Chern and D. C., Spencer on their sixtieth birthdays. (Cited on page 118.)Google Scholar

[80] A., Borel. Introduction aux groupes arithmétiques. Publ. de l'Institut de Math. de l'Université de Strasbourg, XV. Actualités Sci. Ind., No. 1341. Hermann, Paris, 1969. (Cited on page 104.)

[81] A., Borel and Harish-Chandra, . Arithmetic subgroups of algebraic groups. Ann. of Math. (2), 75:485–535, 1962. (Cited on page 339.)Google Scholar

[82] S., Bosch, W., Lütkebohmert, and M., Raynaud. Néron models, vol. 21 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Springer-Verlag, Berlin, 1990. (Cited on pages 86, 199, 238, 239, and 417.)

[83] N., Bourbaki. Lie groups and Lie algebras. Chapters 4–6. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 2002. (Cited on page 152.)

[84] N., Bourbaki. Éléments de mathématique. Algèbre. Chapitre 9. Springer-Verlag, Berlin, 2007. (Cited on page 59.)

[85] A., Bremner. A geometric approach to equal sums of sixth powers. Proc. Lond. Math. Soc. (3), 43(3):544–581, 1981. (Cited on page 390.)Google Scholar

[86] T., Bridgeland. Stability conditions on K3 surfaces. Duke Math. J., 141(2):241–291, 2008. (Cited on pages 375, 376, and 384.)Google Scholar

[87] T., Bridgeland and A., Maciocia. Complex surfaces with equivalent derived categories. Math. Z., 236(4):677–697, 2001. (Cited on page 373.)Google Scholar

[88] T., Bröcker and T. tom, Dieck. Representations of compact Lie groups, vol. 98 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. (Cited on page 59.)

[89] J., Bryan and N. C., Leung. The enumerative geometry of K3 surfaces and modular forms. J. Amer. Math. Soc., 13(2):371–410 (electronic), 2000. (Cited on page 297.)Google Scholar

[90] N., Buchdahl. On compact Kähler surfaces. Ann. Inst. Fourier (Grenoble), 49(1):287–302, 1999. (Cited on pages 135, 137, and 171.)Google Scholar

[91] N., Buchdahl. Compact Kähler surfaces with trivial canonical bundle. Ann. Global Anal. Geom., 23(2):189–204, 2003. (Cited on pages 144 and 146.)Google Scholar

[92] A., Buium. Sur le nombre de Picard des revêtements doubles des surfaces algébriques. C. R. Acad. Sci. Paris Sér. I Math., 296(8):361–364, 1983. (Cited on page 390.)Google Scholar

[93] D., Burns and M., Rapoport. On the Torelli problem for kählerian K3 surfaces. Ann. Sci. École Norm. Sup. (4), 8(2):235–273, 1975. (Cited on pages 44, 116, 133, and 145.)Google Scholar

[94] D. Burns, Jr. and J., Wahl. Local contributions to global deformations of surfaces. Invent. Math., 26:67–88, 1974. (Cited on page 142.)Google Scholar

[95] G., Buzzard and S., Lu. Algebraic surfaces holomorphically dominable by C2. Invent. Math., 139(3):617–659, 2000. (Cited on page 275.)Google Scholar

[96] A., Căldăraru. Derived categories of twisted sheaves on Calabi–Yau manifolds. ProQuest LLC, Ann Arbor, MI, 2000. PhD thesis, Cornell University. (Cited on pages 208, 242, 376, and 377.)

[97] C., Camere. About the stability of the tangent bundle of Pn restricted to a surface. Math. Z., 271(1–2):499–507, 2012. (Cited on pages 179, 186, and 187.)Google Scholar

[98] F., Campana. Orbifolds, special varieties and classification theory. Ann. Inst. Fourier (Grenoble), 54(3):499–630, 2004. (Cited on page 274.)Google Scholar

[99] F., Campana, K., Oguiso, and T., Peternell. Non-algebraic hyperkähler manifolds. J. Differential Geom., 85(3):397–424, 2010. (Cited on page 387.)Google Scholar

[100] A., Canonaco and P., Stellari. Twisted Fourier–Mukai functors. Adv. Math., 212(2):484–503, 2007. (Cited on page 376.)Google Scholar

[101] A., Canonaco and P., Stellari. Fourier–Mukai functors: a survey. In Derived categories in algebraic geometry, EMS Ser. Congr. Rep., pages 27–60. Eur. Math. Soc., Zürich, 2012. (Cited on page 362.)Google Scholar

[102] S., Cantat. Sur la dynamique du groupe d'automorphismes des surfaces K3. Transform. Groups, 6(3):201–214, 2001. (Cited on page 357.)Google Scholar

[103] J., Carlson, S., Müller-Stach, and C., Peters. Period mappings and period domains, vol. 85 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, 2003. (Cited on page 102.)

[104] H., Cartan. Quotient d'un espace analytique par un groupe d'automorphismes. In Algebraic geometry and topology, pages 90–102. Princeton University Press, 1957. A symposium in honor of S. Lefschetz. (Cited on page 331.)

[105] J., Cassels. Rational quadratic forms, vol. 13 of Lond. Math. Soc. Monographs. Academic Press (Harcourt Brace Jovanovich), London, 1978. (Cited on pages 300, 301, and 311.)

[106] J., Cassels and A., Fröhlich, editors. Algebraic number theory. Academic Press (Harcourt Brace Jovanovich), London, 1986. Reprint of the 1967 original. (Cited on pages 420 and 421.)

[107] F., Catanese and B., Wajnryb. Diffeomorphism of simply connected algebraic surfaces. J. Differential Geom., 76(2):177–213, 2007. (Cited on page 129.)Google Scholar

[108] E., Cattani, P., Deligne, and A., Kaplan. On the locus of Hodge classes. J. Amer. Math. Soc., 8(2):483–506, 1995. (Cited on page 122.)Google Scholar

[109] A., Chambert-Loir. Cohomologie cristalline: un survol. Exposition. Math., 16(4):333–382, 1998. (Cited on page 433.)Google Scholar

[110] F., Charles. The Tate conjecture for K3 surfaces over finite fields. Invent. Math., 194(1):119–145, 2013. Erratum 202(1):481–485, 2015. (Cited on page 407.)Google Scholar

[111] F., Charles. Birational boundedness for holomorphic symplectic varieties, Zarhin's trick for K3 surfaces, and the Tate conjecture. 2014. arXiv:1407.0592. (Cited on pages 27, 79, 197, 407, 408, 425, and 426.)

[112] F., Charles. On the Picard number of K3 surfaces over number fields. Algebra Number Theory, 8(1):1–17, 2014. (Cited on page 397.)Google Scholar

[113] F., Charles and C., Schnell. Notes on absolute Hodge classes. In Hodge theory, vol. 49 of Math. Notes, pages 469–530. Princeton University Press, Princeton, NJ, 2014. (Cited on pages 70, 78, and 79.)

[114] X., Chen. Rational curves on K3 surfaces. J. Algebraic Geom., 8(2):245–278, 1999. (Cited on pages 277 and 282.)Google Scholar

[115] X., Chen. A simple proof that rational curves on K3 are nodal. Math. Ann., 324(1):71–104, 2002. (Cited on pages 282 and 297.)Google Scholar

[116] X., Chen. Self rational maps of K3 surfaces. 2010. arXiv:1008.1619. (Cited on page 356.)

[117] X., Chen and J., Lewis. Density of rational curves on K3 surfaces. Math. Ann., 356(1):331–354, 2013. (Cited on page 296.)Google Scholar

[118] J., Choy and Y.-H., Kiem. Nonexistence of a crepant resolution of some moduli spaces of sheaves on a K3 surface. J. Korean Math. Soc., 44(1):35–54, 2007. (Cited on page 217.)Google Scholar

[119] C., Ciliberto and T., Dedieu. On universal Severi varieties of low genus K3 surfaces. Math. Z., 271(3–4):953–960, 2012. (Cited on page 295.)Google Scholar

[120] C., Ciliberto and G., Pareschi. Pencils of minimal degree on curves on a K3 surface. J. Reine Angew. Math., 460:15–36, 1995. (Cited on page 184.)Google Scholar

[121] H., Clemens, J., Kollár, and S., Mori. Higher-dimensional complex geometry, vol. 166 of Astérisque. Soc. Math. France, Paris, 1988. (Cited on page 25.)

[122] J.-L., Colliot-Thélène. Cycles algébriques de torsion et K-théorie algébrique. In Arithmetic algebraic geometry (Trento, 1991), vol. 1553 of Lecture Notes in Math., pages 1–49. Springer-Verlag, Berlin, 1993. (Cited on pages 256, 257, 263, 267, and 270.)

[123] J.-L., Colliot-Thélène. L'arithmétique du groupe de Chow des zéro-cycles. J. Théor. Nombres Bordeaux, 7(1):51–73, 1995. Les Dix-huitièmes Journées Arithmétiques (Bordeaux, 1993). (Cited on page 271.)Google Scholar

[124] J.-L., Colliot-Thélène. Groupe de Chow des zéro-cycles sur les variétés p-adiques [d'après S. Saito, K. Sato et al.], Séminaire Bourbaki, Exposé 1012, 2009/2010. Astérisque, 339: 1–30, 2011. (Cited on page 270.)Google Scholar

[125] J.-L., Colliot-Thélène and W., Raskind. Groupe de Chow de codimension deux des variétés définies sur un corps de nombres: un théorème de finitude pour la torsion. Invent. Math., 105(2):221–245, 1991. (Cited on page 270.)Google Scholar

[126] J.-L., Colliot-Thélène, J.-J., Sansuc, and C., Soulé. Torsion dans le groupe de Chow de codimension deux. Duke Math. J., 50(3):763–801, 1983. (Cited on pages 257, 267, and 271.)Google Scholar

[127] P., Colmez and J.-P., Serre, editors. Correspondance Grothendieck–Serre. Documents Mathématiques, 2. Soc. Math. France, Paris, 2001. (Cited on page 80.)

[128] D., Comenetz. Two algebraic deformations of a K3 surface. Nagoya Math. J., 82:1–26, 1981. (Cited on page 84.)Google Scholar

[129] B., Conrad, M., Lieblich, and M., Olsson. Nagata compactification for algebraic spaces. J. Inst. Math. Jussieu, 11(4):747–814, 2012. (Cited on page 83.)Google Scholar

[130] J., Conway. A group of order 8, 315, 553, 613, 086, 720, 000. Bull. Lond. Math. Soc., 1:79–88, 1969. (Cited on page 328.)Google Scholar

[131] J., Conway. The automorphism group of the 26-dimensional even unimodular Lorentzian lattice. J. Algebra, 80(1):159–163, 1983. (Cited on page 326.)Google Scholar

[132] J., Conway and N., Sloane. Sphere packings, lattices and groups, vol. 290 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, New York, third edition, 1999. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen, and B. B. Venkov. (Cited on pages 299, 312, 324, 325, 326, 327, 328, and 346.)

[133] F., Cossec and I., Dolgachev. Enriques surfaces. I, vol. 76 of Progr. Math. Birkhäuser Boston Inc., 1989. (Cited on pages 219, 242, and 246.)

[134] D., Cox. Mordell–Weil groups of elliptic curves over C(t) with pg = 0 or 1. Duke Math. J., 49(3):677–689, 1982. (Cited on pages 232 and 237.)Google Scholar

[135] D., Cox and S., Zucker. Intersection numbers of sections of elliptic surfaces. Invent. Math., 53(1):1–44, 1979. (Cited on page 237.)Google Scholar

[136] J. de, Jong. A result of Gabber. 2003. Preprint. (Cited on pages 383 and 413.)

[137] J. de, Jong. The period-index problem for the Brauer group of an algebraic surface. Duke Math. J., 123(1):71–94, 2004. (Cited on page 412.)Google Scholar

[138] O., Debarre. Higher-dimensional algebraic geometry. Universitext. Springer-Verlag, New York, 2001. (Cited on page 25.)

[139] O., Debarre. Complex tori and abelian varieties, vol. 11 of SMF/AMS Texts and Monographs. Amer. Math. Soc., Providence, RI, 2005. (Cited on pages 10 and 58.)

[140] T., Dedieu. Severi varieties and self-rational maps of K3 surfaces. Internat. J. Math., 20(12):1455–1477, 2009. (Cited on page 356.)Google Scholar

[141] P., Deligne. La conjecture de Weil pour les surfaces K3. Invent. Math., 15:206–226, 1972. (Cited on pages 68, 73, 74, 78, 79, and 122.)Google Scholar

[142] P., Deligne. Cohomologie étale, vol. 569 of Lecture Notes in Math. Springer-Verlag, Berlin, 1977. Séminaire de Géométrie Algébrique du Bois-Marie SGA 412, Avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J.-L. Verdier. (Cited on page 247.)

[143] P., Deligne. Relèvement des surfaces K3 en caractéristique nulle. In Algebraic surfaces (Orsay, 1976–78), vol. 868 of Lecture Notes in Math., pages 58–79. Springer-Verlag, Berlin and New York, 1981. Prepared for publication by L. Illusie. (Cited on pages 75 and 431.)

[144] P., Deligne and L., Illusie. Relèvements modulo p2 et décomposition du complexe de de Rham. Invent. Math., 89(2):247–270, 1987. (Cited on pages 21, 195, and 196.)Google Scholar

[145] P., Deligne, J., Milne, A., Ogus, and K., Shih. Hodge cycles, motives, and Shimura varieties, vol. 900 of Lecture Notes in Math. Springer-Verlag, Berlin, 1982. (Cited on pages 53, 58, 78, and 79.)

[146] P., Deligne and D., Mumford. The irreducibility of the space of curves of given genus. Inst. Hautes Études Sci. Publ. Math., 36:75–109, 1969. (Cited on pages 84, 94, 96, and 97.)Google Scholar

[147] J.-P., Demailly and M., Paun. Numerical characterization of the Kähler cone of a compact Kähler manifold. Ann. of Math. (2), 159(3):1247–1274, 2004. (Cited on pages 136, 171, and 172.)Google Scholar

[148] J., Dillies. On some order 6 non-symplectic automorphisms of elliptic K3 surfaces. Albanian J. Math., 6(2):103–114, 2012. (Cited on page 356.)Google Scholar

[149] I., Dolgachev. Integral quadratic forms: applications to algebraic geometry [after V. Nikulin], Séminaire Bourbaki, Exposé 611, 1982/1983. Astérisque, 105:251–278, 1983. (Cited on pages 170 and 299.)Google Scholar

[150] I., Dolgachev. Mirror symmetry for lattice polarized K3 surfaces. J. Math. Sci., 81(3):2599–2630, 1996. Algebraic geometry, 4. (Cited on pages 99, 127, and 279.)Google Scholar

[151] I., Dolgachev. Classical algebraic geometry – a modern view. Cambridge University Press, Cambridge, 2012. (Cited on page 15.)

[152] I., Dolgachev and J., Keum. Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic. Ann. of Math. (2), 169(1):269–313, 2009. (Cited on page 334.)Google Scholar

[153] I., Dolgachev and J., Keum. K3 surfaces with a symplectic automorphism of order 11. J. Eur. Math. Soc. (JEMS), 11(4):799–818, 2009. (Cited on page 335.)Google Scholar

[154] I., Dolgachev and S., Kondō. Moduli of K3 surfaces and complex ball quotients. In Arithmetic and geometry around hypergeometric functions, vol. 260 of Progr. Math., pages 43–100. Birkhäuser, Basel, 2007. (Cited on pages 99 and 127.)

[155] R., Donagi and D., Morrison. Linear systems on K3-sections. J. Differential Geom., 29(1):49–64, 1989. (Cited on page 184.)Google Scholar

[156] R., Donagi and T., Pantev. Torus fibrations, gerbes, and duality. Mem. Amer. Math. Soc., 193(901):vi+90, 2008. With an appendix by D. Arinkin. (Cited on pages 250 and 383.)Google Scholar

[157] S., Donaldson. Polynomial invariants for smooth four-manifolds. Topology, 29(3):257–315, 1990. (Cited on page 144.)Google Scholar

[158] S., Donaldson. Scalar curvature and projective embeddings. I. J. Differential Geom., 59(3):479–522, 2001. (Cited on page 98.)Google Scholar

[159] P., Duhem. Émile Mathieu, his life and works. Bull. Amer. Math. Soc., 1(7):156–168, 1892. (Cited on page 345.)Google Scholar

[160] W., Ebeling. The monodromy groups of isolated singularities of complete intersections, vol. 1293 of Lecture Notes in Math. Springer-Verlag, Berlin, 1987. (Cited on page 312.)

[161] W., Ebeling. Lattices and codes. Advanced Lectures in Mathematics. Friedr. Vieweg & Sohn Braunschweig, revised edition, 2002. A course partially based on lectures by F. Hirzebruch. (Cited on pages 299, 301, 304, and 325.)

[162] D., Edidin. Notes on the construction of the moduli space of curves. In Recent progress in intersection theory (Bologna, 1997), Trends Math., pages 85–113. Birkhäuser, Boston, 2000. (Cited on page 97.)

[163] M., Eichler. Quadratische Formen und orthogonale Gruppen, vol. 63 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, second edition, 1974. (Cited on pages 299 and 308.)

[164] L., Ein and R., Lazarsfeld. Stability and restrictions of Picard bundles, with an application to the normal bundles of elliptic curves. In Complex projective geometry (Trieste, 1989/Bergen, 1989), vol. 179 of Lond. Math. Soc. Lecture Note Ser., pages 149–156. Cambridge University Press, 1992. (Cited on page 187.)

[165] T., Ekedahl. Foliations and inseparable morphisms. In Algebraic geometry, Bowdoin, 1985 (Brunswick, ME, 1985), vol. 46 of Proc. Sympos. Pure Math., pages 139–149. Amer. Math. Soc., Providence, RI, 1987. (Cited on page 190.)

[166] T., Ekedahl and G. van der, Geer. Cycle classes on the moduli of K3 surfaces in positive characteristic. Selecta Math. (N.S.), 21(1):245–291, 2015. (Cited on pages 435 and 437.)Google Scholar

[167] F. El, Zein. Introduction à la théorie de Hodge mixte. Actualités Mathématiques. Hermann, Paris, 1991. (Cited on pages 58 and 102.)

[168] J., Ellenberg. K3 surfaces over number fields with geometric Picard number one. In Arithmetic of higher-dimensional algebraic varieties (Palo Alto, CA, 2002), vol. 226 of Progr. Math., pages 135–140. Birkhäuser, Boston, 2004. (Cited on pages 315, 398, and 399.)

[169] A., Elsenhans and J., Jahnel. On the computation of the Picard group for K3 surfaces. Math. Proc. Cambridge Philos. Soc., 151(2):263–270, 2011. (Cited on page 401.)Google Scholar

[170] A., Elsenhans and J., Jahnel. The Picard group of a K3 surface and its reduction modulo p. Algebra Number Theory, 5(8):1027–1040, 2011. (Cited on pages 397 and 401.)Google Scholar

[171] A., Elsenhans and J., Jahnel. Examples of K3 surfaces with real multiplication. LMS J. Comput. Math., 17(suppl. A):14–35, 2014. (Cited on page 58.)Google Scholar

[172] H., Esnault and K., Oguiso. Non-liftability of automorphism groups of a K3 surface in positive characteristic. Math. Ann., 363(3–4):1187–1206, 2015. (Cited on page 357.)Google Scholar

[173] H., Esnault and V., Srinivas. Algebraic versus topological entropy for surfaces over finite fields. Osaka J. Math., 50(3):827–846, 2013. (Cited on page 335.)Google Scholar

[174] J., Esser. Noether–Lefschetz-Theoreme für zyklische Überlagerungen. University Essen, Fachbereich Mathematik und Informatik, Essen, 1993. (Cited on page 390.)

[175] G., Faltings, G., Wüstholz, F., Grunewald, N., Schappacher, and U., Stuhler. Rational points. Aspects of Mathematics, E6. Friedr. Vieweg & Sohn, Braunschweig, third edition, 1992. (Cited on pages 233, 405, and 406.)

[176] B., Fantechi, L., Göttsche, L., Illusie, S., Kleiman, N., Nitsure, and A., Vistoli. Fundamental algebraic geometry, Grothendieck's FGA explained, vol. 123 of Mathematical Surveys and Monographs. Amer. Math. Soc., Providence, RI, 2005. (Cited on pages 86, 93, 195, 199, 204, 238, 239, 397, 416, 417, and 418.)

[177] B., Fantechi, L., Göttsche, and D. van, Straten. Euler number of the compactified Jacobian and multiplicity of rational curves. J. Algebraic Geom., 8(1):115–133, 1999. (Cited on page 294.)Google Scholar

[178] D., Festi, A., Garbagnati, B. van, Geemen, and R. van, Luijk. The Cayley–Oguiso automorphism of positive entropy on a K3 surface. J. Mod. Dyn., 7(1):75–97, 2013. (Cited on page 343.)Google Scholar

[179] J.-M., Fontaine. Groupes p-divisibles sur les corps locaux. Société Mathématique de France, Paris, 1977. Astérisque, No. 47-48. (Cited on page 433.)

[180] K., Frantzen. Classification of K3 surfaces with involution and maximal symplectic symmetry. Math. Ann., 350(4):757–791, 2011. (Cited on page 356.)Google Scholar

[181] R., Friedman. A degenerating family of quintic surfaces with trivial monodromy. Duke Math. J., 50(1):203–214, 1983. (Cited on page 126.)Google Scholar

[182] R., Friedman. Global smoothings of varieties with normal crossings. Ann. of Math. (2), 118(1):75–114, 1983. (Cited on page 126.)Google Scholar

[183] R., Friedman. A new proof of the global Torelli theorem for K3 surfaces. Ann. of Math. (2), 120(2):237–269, 1984. (Cited on pages 99, 116, 127, and 146.)Google Scholar

[184] R., Friedman. On threefolds with trivial canonical bundle. In Complex geometry and Lie theory (Sundance, UT, 1989), vol. 53 of Proc. Sympos. Pure Math., pages 103–134. Amer. Math. Soc., Providence, RI, 1991. (Cited on page 142.)

[185] R., Friedman. Algebraic surfaces and holomorphic vector bundles. Universitext. Springer Verlag, New York, 1998. (Cited on pages 15, 175, 198, and 221.)

[186] R., Friedman and J., Morgan. Smooth four-manifolds and complex surfaces, vol. 27 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Springer-Verlag, Berlin, 1994. (Cited on pages 13, 15, 129, 219, 226, 244, 247, and 252.)

[187] R., Friedman and D., Morrison. The birational geometry of degenerations: an overview. In The birational geometry of degenerations (Cambridge, MA, 1981), vol. 29 of Progr. Math., pages 1–32. Birkhäuser, Boston, 1983. (Cited on pages 125 and 126.)

[188] R., Friedman and F., Scattone. Type III degenerations of K3 surfaces. Invent. Math., 83(1):1–39, 1986. (Cited on page 126.)Google Scholar

[189] A., Fujiki. On automorphism groups of compact Kähler manifolds. Invent. Math., 44(3):225–258, 1978. (Cited on page 337.)Google Scholar

[190] A., Fujiki. Finite automorphism groups of complex tori of dimension two. Publ. Res. Inst. Math. Sci., 24(1):1–97, 1988. (Cited on page 329.)Google Scholar

[191] T., Fujita. On polarized manifolds whose adjoint bundles are not semipositive. In Algebraic geometry, Sendai, 1985, vol. 10 of Adv. Stud. Pure Math., pages 167–178. North-Holland, Amsterdam, 1987. (Cited on page 24.)

[192] W., Fulton. Intersection theory, vol. 2 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Springer-Verlag, Berlin, second edition, 1998. (Cited on pages 254, 255, 256, and 259.)

[193] W., Fulton and R., Pandharipande. Notes on stable maps and quantum cohomology. In Algebraic geometry – Santa Cruz 1995, vol. 62 of Proc. Sympos. Pure Math., pages 45–96. Amer. Math. Soc., Providence, RI, 1997. (Cited on page 286.)

[194] P., Gabriel. Des catégories abéliennes. Bull. Soc. Math. France, 90:323–448, 1962. (Cited on page 358.)Google Scholar

[195] C., Galati and A., Knutsen. Seshadri constants of K3 surfaces of degrees 6 and 8. Int. Math. Res. Not. IMRN, 17:4072–4084, 2013. (Cited on page 34.)Google Scholar

[196] F., Galluzzi. Abelian fourfold of Mumford-type and Kuga–Satake varieties. Indag. Math. (N.S.), 11(4):547–560, 2000. (Cited on page 79.)Google Scholar

[197] F., Galluzzi and G., Lombardo. On automorphisms group of some K3 surfaces. Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 142:109–120 (2009), 2008. (Cited on pages 342 and 343.)Google Scholar

[198] F., Galluzzi, G., Lombardo, and C., Peters. Automorphs of indefinite binary quadratic forms and K3 surfaces with Picard number 2. Rend. Semin. Mat. Univ. Politec. Torino, 68(1):57–77, 2010. (Cited on pages 341 and 343.)Google Scholar

[199] A., Garbagnati. Symplectic automorphisms on Kummer surfaces. Geom. Dedicata, 145:219–232, 2010. (Cited on page 352.)Google Scholar

[200] A., Garbagnati. On K3 surface quotients of K3 or abelian surfaces. 2015. arXiv:1507.03824. (Cited on page 329.)

[201] A., Garbagnati and A., Sarti. Symplectic automorphisms of prime order on K3 surfaces. J. Algebra, 318(1):323–350, 2007. (Cited on pages 99, 352, and 353.)Google Scholar

[202] A., Garbagnati and A., Sarti. On symplectic and non-symplectic automorphisms of K3 surfaces. Rev. Mat. Iberoam., 29(1):135–162, 2013. (Cited on page 356.)Google Scholar

[203] B. van, Geemen. Kuga–Satake varieties and the Hodge conjecture. In The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), vol. 548 of NATO Sci. Ser. C Math. Phys. Sci., pages 51–82. Kluwer Academic, Dordrecht, 2000. (Cited on pages 39, 41, 53, 58, 65, 66, and 68.)

[204] B. van, Geemen. Real multiplication on K3 surfaces and Kuga–Satake varieties. Michigan Math. J., 56(2):375–399, 2008. (Cited on pages 52, 54, 58, and 79.)Google Scholar

[205] B. van, Geemen and A., Sarti. Nikulin involutions on K3 surfaces. Math. Z., 255(4):731–753, 2007. (Cited on pages 99, 353, and 355.)Google Scholar

[206] G. van der, Geer and T., Katsura. Note on tautological classes of moduli of K3 surfaces. Mosc. Math. J., 5(4):775–779, 972, 2005. (Cited on page 99.)Google Scholar

[207] I., Gelfand, M., Kapranov, and A., Zelevinsky. Discriminants, resultants and multidimensional determinants. Modern Birkhäuser Classics. Birkhäuser, Boston 2008. (Cited on page 389.)

[208] S., Gelfand and Y., Manin. Methods of homological algebra. Springer Monographs in Mathematics. Springer-Verlag,Berlin, second edition, 2003. (Cited on pages 258 and 358.)

[209] J., Giansiracusa. The diffeomorphism group of a K3 surface and Nielsen realization. J. Lond. Math. Soc. (2), 79(3):701–718, 2009. (Cited on pages 144 and 145.)Google Scholar

[210] J., Giraud. Cohomologie non abélienne, vol. 179 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin and New York, 1971. (Cited on pages 383 and 412.)

[211] M., Gonzalez-Dorrego. (16, 6) configurations and geometry of Kummer surfaces in P3. Mem. Amer. Math. Soc., 107(512):vi+101, 1994. (Cited on page 15.)Google Scholar

[212] L., Göttsche. The Betti numbers of the Hilbert scheme of points on a smooth projective surface. Math. Ann., 286(1-3):193–207, 1990. (Cited on page 217.)Google Scholar

[213] L., Göttsche. A conjectural generating function for numbers of curves on surfaces. Comm. Math. Phys., 196(3):523–533, 1998. (Cited on page 297.)Google Scholar

[214] L., Göttsche and D., Huybrechts. Hodge numbers of moduli spaces of stable bundles on K3 surfaces. Internat. J. Math., 7(3):359–372, 1996. (Cited on page 216.)Google Scholar

[215] H., Grauert. On the number of moduli of complex structures. In Contributions to function theory (Internat. Colloq. Function Theory, Bombay, 1960), pages 63–78. Tata Institute of Fundamental Research, Bombay, 1960. (Cited on pages xi and 109.)

[216] M., Green and P., Griffiths. Two applications of algebraic geometry to entire holomorphic mappings. In The Chern Symposium 1979, pages 41–74. Springer-Verlag, New York, 1980. (Cited on page 297.)

[217] M., Green, P., Griffiths, and K., Paranjape. Cycles over fields of transcendence degree 1. Michigan Math. J., 52(1):181–187, 2004. (Cited on pages 264 and 265.)Google Scholar

[218] M., Green and R., Lazarsfeld. Special divisors on curves on a K3 surface. Invent. Math., 89(2):357–370, 1987. (Cited on page 184.)Google Scholar

[219] P., Griffiths. Periods of integrals on algebraic manifolds: summary of main results and discussion of open problems. Bull. Amer. Math. Soc., 76:228–296, 1970. (Cited on pages 126 and 147.)Google Scholar

[220] P., Griffiths, editor. Topics in transcendental algebraic geometry, vol. 106 of Annals of Mathematics Studies, Princeton University Press, Princeton, NJ, 1984. (Cited on page 102.)

[221] P., Griffiths and J., Harris. Principles of algebraic geometry.Wiley-Interscience, New York, 1978. (Cited on pages 43, 58, 171, 332, and 333.)

[222] P., Griffiths and J., Harris. On the variety of special linear systems on a general algebraic curve. Duke Math. J., 47(1):233–272, 1980. (Cited on page 183.)Google Scholar

[223] V., Gritsenko, K., Hulek, and G., Sankaran. The Kodaira dimension of the moduli of K3 surfaces. Invent. Math., 169(3):519–567, 2007. (Cited on page 99.)Google Scholar

[224] V., Gritsenko, K., Hulek, and G., Sankaran. Abelianisation of orthogonal groups and the fundamental group of modular varieties. J. Algebra, 322(2):463–478, 2009. (Cited on page 308.)Google Scholar

[225] A., Grothendieck. Fondements de la géométrie algébrique. [Extraits du Séminaire Bourbaki, 1957–1962.]. Secrétariat Mathématique, Paris, 1962. (Cited on pages 85, 93, 204, and 397.)

[226] A., Grothendieck. Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas IV. Inst. Hautes Études Sci. Publ. Math., 32:361, 1967. (Cited on page 98.)Google Scholar

[227] A., Grothendieck. Le groupe de Brauer. III. Exemples et compléments. In Dix Exposés sur la Cohomologie des Schémas, pages 88–188. North-Holland, Amsterdam, 1968. (Cited on pages 247, 249, 410, and 413.)

[228] A., Grothendieck. Technique de descente et théorèmes d'existence en géométrie algébrique. II. Le théorème d'existence en théorie formelle des modules. In Séminaire Bourbaki, Vol. 5, Exp. No. 195, pages 369–390. Soc. Math. France, Paris, 1995. (Cited on page 330.)

[229] M., Halic. A remark about the rigidity of curves on K3 surfaces. Collect. Math., 61(3):323–336, 2010. (Cited on page 297.)Google Scholar

[230] M., Halic. Some remarks about curves on K3 surfaces. In Teichmüller theory and moduli problem, vol. 10 of Ramanujan Math. Soc. Lect. Notes Ser., pages 373–385. Ramanujan Math. Soc., Mysore, 2010. (Cited on page 297.)

[231] A., Harder and A., Thompson. The geometry and moduli of K3 surfaces. 2015. arXiv:1501.04049. (Cited on page 126.)

[232] J., Harris. Galois groups of enumerative problems. Duke Math. J., 46(4):685–724, 1979. (Cited on pages 295 and 399.)Google Scholar

[233] J., Harris and I., Morrison. Moduli of curves, vol. 187 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1998. (Cited on pages 283 and 285.)

[234] R., Hartshorne. Residues and duality, vol. 20 of Lecture Notes in Math. Springer-Verlag, Berlin, 1966. Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/1964. With an appendix by P. Deligne. (Cited on page 6.)

[235] R., Hartshorne. Ample subvarieties of algebraic varieties, vol. 156 of Lecture Notes in Math. Springer-Verlag, Berlin, 1970. Notes written in collaboration with C. Musili. (Cited on pages 2, 4, 19, and 149.)

[236] R., Hartshorne. Algebraic geometry, vol. 52 of Graduate Texts in Mathematics. Springer- Verlag, New York, 1977. (Cited on pages 2, 3, 4, 5, 6, 8, 17, 19, 24, 27, 28, 29, 32, 73, 149, 189, 213, 219, 221, 222, 239, 254, 255, 262, 295, and 434.)

[237] R., Hartshorne. Deformation theory, vol. 257 of Graduate Texts in Mathematics. Springer- Verlag, New York, 2010. (Cited on pages 92, 110, and 416.)

[238] K., Hashimoto. Finite symplectic actions on the K3 lattice. Nagoya Math. J., 206:99–153, 2012. (Cited on pages 344 and 352.)Google Scholar

[239] B., Hassett. Rational curves on K3 surfaces. Lecture notes. (Cited on pages 272, 273, and 281.)

[240] B., Hassett. Special cubic fourfolds. Compositio Math., 120(1):1–23, 2000. (Cited on pages 306, 308, and 309.)Google Scholar

[241] B., Hassett, A., Kresch, and Y., Tschinkel. Effective computation of Picard groups and Brauer–Manin obstructions of degree two K3 surfaces over number fields. Rend. Circ. Mat. Palermo (2), 62(1):137–151, 2013. (Cited on page 437.)Google Scholar

[242] B., Hassett and Y., Tschinkel. Rational points on K3 surfaces and derived equivalence. 2014. arXiv:1411.6259. (Cited on pages 126 and 379.)

[243] N., Hitchin, A., Karlhede, U., Lindström, and M., Roček. Hyper-Kähler metrics and supersymmetry. Comm. Math. Phys., 108(4):535–589, 1987. (Cited on page 136.)Google Scholar

[244] E., Horikawa. Surjectivity of the period map of K3 surfaces of degree 2. Math. Ann., 228(2):113–146, 1977. (Cited on page 116.)Google Scholar

[245] S., Hosono, B., Lian, K., Oguiso, and S.-T., Yau. Kummer structures on K3 surface: an old question of T. Shioda. Duke Math. J., 120(3):635–647, 2003. (Cited on page 373.)Google Scholar

[246] S., Hosono, B., Lian, K., Oguiso, and S.-T., Yau. Autoequivalences of derived category of a K3 surface and monodromy transformations. J. Algebraic Geom., 13(3):513–545, 2004. (Cited on page 374.)Google Scholar

[247] S., Hosono, B. H., Lian, K., Oguiso, and S.-T., Yau. Fourier–Mukai partners of a K3 surface of Picard number one. In Vector bundles and representation theory (Columbia, MO, 2002), vol. 322 of Contemp. Math., pages 43–55. Amer. Math. Soc., Providence, RI, 2003. (Cited on pages 218 and 384.)

[248] R., Hudson. Kummer's quartic surface. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1990. With a foreword by W. Barth, revised reprint of the 1905 original. (Cited on page 15.)

[249] K., Hulek and D., Ploog. Fourier–Mukai partners and polarised K3 surfaces. In Arithmetic and geometry of K3 surfaces and Calabi–Yau threefolds, vol. 67 of Fields Inst. Commun., pages 333–365. Springer-Verlag, New York, 2013. (Cited on page 384.)

[250] D., Huybrechts. Compact hyperkähler manifolds: basic results. Invent. Math., 135(1):63–113, 1999. (Cited on pages 115, 133, 138, 217, and 294.)Google Scholar

[251] D., Huybrechts. Compact hyperkähler manifolds. In Calabi–Yau manifolds and related geometries (Nordfjordeid, 2001), Universitext, pages 161–225. Springer-Verlag, Berlin, 2003. (Cited on pages 147 and 216.)

[252] D., Huybrechts. Moduli spaces of hyperkähler manifolds and mirror symmetry. In Intersection theory and moduli, ICTP Lect. Notes, XIX, pages 185–247 (electronic). Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2004. (Cited on pages 140 and 314.)

[253] D., Huybrechts. Complex geometry. Universitext. Springer-Verlag, Berlin, 2005. (Cited on pages 39, 40, 41, 58, 171, 191, and 192.)

[254] D., Huybrechts. Fourier–Mukai transforms in algebraic geometry. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, Oxford, 2006. (Cited on pages 214, 358, 361, 362, 363, 364, 367, 370, 371, and 374.)

[255] D., Huybrechts. Derived and abelian equivalence of K3 surfaces. J. Algebraic Geom., 17(2):375–400, 2008. (Cited on page 372.)Google Scholar

[256] D., Huybrechts. The global Torelli theorem: classical, derived, twisted. In Algebraic geometry – Seattle 2005. Part 1, vol. 80 of Proc. Sympos. Pure Math., pages 235–258. Amer. Math. Soc., Providence, RI, 2009. (Cited on pages 377 and 382.)

[257] D., Huybrechts. Chow groups of K3 surfaces and spherical objects. J. Eur. Math. Soc. (JEMS), 12(6):1533–1551, 2010. (Cited on pages 269 and 270.)Google Scholar

[258] D., Huybrechts. A note on the Bloch–Beilinson conjecture for K3 surfaces and spherical objects. Pure Appl. Math. Q., 7(4, Special Issue: In memory of Eckart Viehweg): 1395–1405, 2011. (Cited on page 271.)Google Scholar

[259] D., Huybrechts. A global Torelli theorem for hyperkähler manifolds [after M. Verbitsky], Séminaire Bourbaki, Exposé 1040, 2010/2011. Astérisque, 348:375–403, 2012. (Cited on pages 128, 132, 133, 135, and 139.)Google Scholar

[260] D., Huybrechts. Symplectic automorphisms of K3 surfaces of arbitrary finite order. Math. Res. Lett., 19(4):947–951, 2012. (Cited on pages 271 and 357.)Google Scholar

[261] D., Huybrechts. On derived categories of K3 surfaces and Mathieu groups. 2013. arXiv:1309.6528. (Cited on pages 349 and 384.)

[262] D., Huybrechts. Curves and cycles on K3 surfaces. Algebraic Geometry, 1(1):69–106, 2014. With an appendix by C. Voisin. (Cited on pages 267 and 269.)Google Scholar

[263] D., Huybrechts. Introduction to stability conditions. In Moduli spaces, vol. 411 of Lond. Math. Soc. Lecture Note Ser., pages 179–229. Cambridge University Press, 2014. (Cited on pages 375 and 384.)

[264] D., Huybrechts. The K3 category of a cubic fourfold. 2015. arXiv:1505.01775. (Cited on page 384.)

[265] D., Huybrechts and M., Kemeny. Stable maps and Chow groups. Doc. Math., 18:507–517, 2012. (Cited on pages 271, 286, and 357.)Google Scholar

[266] D., Huybrechts and M., Lehn. The geometry of moduli spaces of sheaves. Cambridge Mathematical Library. Cambridge University Press, Cambridge, second edition, 2010. (Cited on pages 175, 176, 179, 180, 181, 182, 186, 199, 203, 204, 207, 208, 209, 210, 212, 213, 214, 215, 216, 218, and 243.)

[267] D., Huybrechts, E., Macrì, and P., Stellari. Stability conditions for generic K3 categories. Compositio Math., 144(1):134–162, 2008. (Cited on pages 378, 381, and 382.)Google Scholar

[268] D., Huybrechts, E., Macrì, and P., Stellari. Derived equivalences of K3 surfaces and orientation. Duke Math. J., 149(3):461–507, 2009. (Cited on pages 374 and 382.)Google Scholar

[269] D., Huybrechts and M., Nieper-Wißkirchen. Remarks on derived equivalences of Ricci-flat manifolds. Math. Z., 267(3-4):939–963, 2011. (Cited on pages 13 and 216.)Google Scholar

[270] D., Huybrechts and S., Schröer. The Brauer group of analytic K3 surfaces. Int. Math. Res. Not., 50:2687–2698, 2003. (Cited on pages 412 and 415.)Google Scholar

[271] D., Huybrechts and P., Stellari. Equivalences of twisted K3 surfaces. Math. Ann., 332(4):901–936, 2005. (Cited on pages 378 and 426.)Google Scholar

[272] D., Huybrechts and P., Stellari. Proof of Căldăraru's conjecture. Appendix: “Moduli spaces of twisted sheaves on a projective variety” by K. Yoshioka. In Moduli spaces and arithmetic geometry, vol. 45 of Adv. Stud. Pure Math., pages 31–42. Math. Soc. Japan, Tokyo, 2006. (Cited on page 377.)

[273] E., Ieronymou, A., Skorobogatov, and Y., Zarhin. On the Brauer group of diagonal quartic surfaces. J. Lond. Math. Soc. (2), 83(3):659–672, 2011. With an appendix by P. Swinnerton-Dyer. (Cited on page 321.)Google Scholar

[274] J., Igusa. Betti and Picard numbers of abstract algebraic surfaces. Proc. Nat. Acad. Sci. U.S.A., 46:724–726, 1960. (Cited on page 393.)Google Scholar

[275] H., Inose. Defining equations of singular K3 surfaces and a notion of isogeny. In Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), pages 495–502. Kinokuniya Book Store, Tokyo, 1978. (Cited on page 323.)

[276] H., Ito. On automorphisms of supersingular K3 surfaces. Osaka J. Math., 34(3):713–724, 1997. (Cited on page 341.)Google Scholar

[277] B., Iversen. Cohomology of sheaves. Universitext. Springer-Verlag, Berlin, 1986. (Cited on page 12.)

[278] D., James. On Witt's theorem for unimodular quadratic forms. Pacific J. Math., 26:303–316, 1968. (Cited on page 308.)Google Scholar

[279] U., Jannsen. Mixed motives and algebraic K-theory, vol. 1400 of Lecture Notes in Math. Springer-Verlag, Berlin, 1990. With appendices by S. Bloch and C. Schoen. (Cited on page 261.)

[280] J.-P., Jouanolou. Théorèmes de Bertini et applications, vol. 42 of Progr. Math. Birkhäuser, Boston, 1983. (Cited on page 27.)

[281] D., Kaledin, M., Lehn, and C., Sorger. Singular symplectic moduli spaces. Invent. Math., 164(3):591–614, 2006. (Cited on pages 210 and 217.)Google Scholar

[282] A., Kas. Weierstrass normal forms and invariants of elliptic surfaces. Trans. Amer. Math. Soc., 225:259–266, 1977. (Cited on pages 226 and 229.)Google Scholar

[283] T., Katsura. On Kummer surfaces in characteristic 2. In Proc. Int. Sympos Algebraic Geom. (Kyoto Univ., 1977), pages 525–542. Kinokuniya Book Store, Tokyo, 1978. (Cited on page 3.)

[284] T., Katsura. Generalized Kummer surfaces and their unirationality in characteristic p. J. Fac. Sci. University Tokyo Sect. IA Math., 34(1):1–41, 1987. (Cited on page 329.)Google Scholar

[285] N., Katz. Review of adic cohomology. In Motives (Seattle, WA, 1991), vol. 55 of Proc. Sympos. Pure Math., pages 21–30. Amer. Math. Soc., Providence, RI, 1994. (Cited on page 74.)

[286] N., Katz and W., Messing. Some consequences of the Riemann hypothesis for varieties over finite fields. Invent. Math., 23:73–77, 1974. (Cited on page 436.)Google Scholar

[287] Y., Kawamata. On the cone of divisors of Calabi–Yau fiber spaces. Internat. J. Math., 8(5):665–687, 1997. (Cited on pages 160, 167, and 168.)Google Scholar

[288] K., Kawatani. A hyperbolic metric and stability conditions on K3 surfaces with ρ = 1. 2012. arXiv:1204.1128. (Cited on page 376.)

[289] S., Keel and S., Mori. Quotients by groupoids. Ann. of Math. (2), 145(1):193–213, 1997. (Cited on pages 83, 84, 90, 98, and 204.)Google Scholar

[290] G., Kempf, F., Knudsen, D., Mumford, and B., Saint-Donat. Toroidal embeddings. I. Lecture Notes in Mathematics, vol. 339. Springer-Verlag, Berlin and New York, 1973. (Cited on page 125.)

[291] J., Keum. A note on elliptic K3 surfaces. Trans. Amer. Math. Soc., 352(5):2077–2086, 2000. (Cited on pages 242 and 253.)Google Scholar

[292] J., Keum. Orders of automorphisms of K3 surfaces. 2012. arXiv:1203.5616v8. (Cited on pages 335, 337, 338, and 346.)

[293] V., Kharlamov. Topology, moduli and automorphisms of real algebraic surfaces. Milan J. Math., 70:25–37, 2002. (Cited on pages x and 147.)Google Scholar

[294] F., Kirwan. Moduli spaces of degree d hypersurfaces in Pn. Duke Math. J., 58(1):39–78, 1989. (Cited on page 99.)Google Scholar

[295] S., Kleiman. The standard conjectures. In Motives (Seattle, WA, 1991), vol. 55 of Proc. Sympos. Pure Math., pages 3–20. Amer. Math. Soc., Providence, RI, 1994. (Cited on page 73.)

[296] A., Klemm, D., Maulik, R., Pandharipande, and E., Scheidegger. Noether–Lefschetz theory and the Yau–Zaslow conjecture. J. Amer. Math. Soc., 23(4):1013–1040, 2010. (Cited on page 297.)Google Scholar

[297] R., Kloosterman. Classification of all Jacobian elliptic fibrations on certain K3 surfaces. J. Math. Soc. Japan, 58(3):665–680, 2006. (Cited on page 253.)Google Scholar

[298] R., Kloosterman. Elliptic K3 surfaces with geometric Mordell–Weil rank 15. Canad. Math. Bull., 50(2):215–226, 2007. (Cited on pages 237 and 401.)Google Scholar

[299] A., Knapp. Advanced algebra. Cornerstones. Birkhäuser, Boston, 2007. (Cited on page 411.)

[300] M., Kneser. Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen. Arch. Math. (Basel), 7:323–332, 1956. (Cited on page 307.)Google Scholar

[301] M., Kneser. Erzeugung ganzzahliger orthogonaler Gruppen durch Spiegelungen. Math. Ann., 255(4):453–462, 1981. (Cited on page 312.)Google Scholar

[302] M., Kneser. Quadratische Formen. Springer-Verlag, Berlin, 2002. Revised and edited in collaboration with Rudolf Scharlau. (Cited on pages 299 and 300.)

[303] A., Knutsen and A., Lopez. A sharp vanishing theorem for line bundles on K3 or Enriques surfaces. Proc. Amer. Math. Soc., 135(11):3495–3498, 2007. (Cited on page 33.)Google Scholar

[304] S., Kobayashi. First Chern class and holomorphic tensor fields. Nagoya Math. J., 77:5–11, 1980. (Cited on page 193.)Google Scholar

[305] S., Kobayashi. Differential geometry of complex vector bundles, vol. 15 of Publications of the Math. Soc. of Japan. Princeton University Press, Princeton, NJ, 1987. Kanô Memorial Lectures, 5. (Cited on pages 191 and 192.)

[306] S., Kobayashi. Transformation groups in differential geometry. Classics in Mathematics. Springer-Verlag, Berlin, 1995. Reprint of the 1972 edition. (Cited on page 330.)

[307] K., Kodaira. On compact analytic surfaces. II, III. Ann. of Math. (2) 77 (1963), 563–626; ibid., 78:1–40, 1963. (Cited on pages 225 and 244.)Google Scholar

[308] K., Kodaira. On the structure of compact complex analytic surfaces. I. Amer. J. Math., 86:751–798, 1964. (Cited on pages xi, 109, and 129.)Google Scholar

[309] K., Kodaira. On homotopy K3 surfaces. In Essays on topology and related topics (Mémoires dédiés à Georges de Rham), pages 58–69. Springer-Verlag, New York, 1970. (Cited on page 13.)

[310] K., Kodaira. Complex manifolds and deformation of complex structures, vol. 283 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, New York, 1986.With an appendix by D. Fujiwara. (Cited on page 109.)

[311] K., Koike, H., Shiga, N., Takayama, and T., Tsutsui. Study on the family of K3 surfaces induced from the lattice (D4)3. Internat. J. Math., 12(9):1049–1085, 2001. (Cited on page 79.)Google Scholar

[312] J., Kollár. Rational curves on algebraic varieties, vol. 32 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Springer-Verlag, Berlin, 1996. (Cited on pages 92, 189, 260, and 286.)

[313] J., Kollár. Quotient spaces modulo algebraic groups. Ann. of Math. (2), 145(1):33–79, 1997. (Cited on page 83.)Google Scholar

[314] J., Kollár. Non-quasi-projective moduli spaces. Ann. of Math. (2), 164(3):1077–1096, 2006. (Cited on page 91.)Google Scholar

[315] J., Kollár and N., Shepherd-Barron. Threefolds and deformations of surface singularities. Invent. Math., 91(2):299–338, 1988. (Cited on page 127.)Google Scholar

[316] J., Kollár et al. Flips and abundance for algebraic threefolds, vol. 211 of Astérisque. Soc. Math. France, Paris, 1992. (Cited on page 188.)

[317] S., Kondō. Enriques surfaces with finite automorphism groups. Japan. J. Math. (N.S.), 12(2):191–282, 1986. (Cited on page 356.)Google Scholar

[318] S., Kondō. On algebraic K3 surfaces with finite automorphism groups. Proc. Japan Acad. Ser. A Math. Sci., 62(9):353–355, 1986. (Cited on page 342.)Google Scholar

[319] S., Kondō. On automorphisms of algebraic K3 surfaces which act trivially on Picard groups. Proc. Japan Acad. Ser. A Math. Sci., 62(9):356–359, 1986. (Cited on pages 336 and 337.)Google Scholar

[320] S., Kondō. Algebraic K3 surfaces with finite automorphism groups. Nagoya Math. J., 116:1–15, 1989. (Cited on page 342.)Google Scholar

[321] S., Kondō. Quadratic forms and K3. Enriques surfaces [translation of Sûgaku 42(1990), no. 4, 346–360; MR1083944 (92b:14018)]. Sugaku Expositions, 6(1):53–72, 1993. Sugaku Expositions. (Cited on pages 335, 337, and 341.)Google Scholar

[322] S., Kondō. Niemeier lattices, Mathieu groups, and finite groups of symplectic automorphisms of K3 surfaces. Duke Math. J., 92(3):593–603, 1998. With an appendix by S. Mukai. (Cited on pages 325, 345, 347, and 350.)Google Scholar

[323] S., Kondō. The maximum order of finite groups of automorphisms of K3 surfaces. Amer. J. Math., 121(6):1245–1252, 1999. (Cited on page 345.)Google Scholar

[324] S., Kondō. Maximal subgroups of the Mathieu group M23 and symplectic automorphisms of supersingular K3 surfaces. Int. Math. Res. Not., Art. ID 71517, 9, 2006. (Cited on page 345.)Google Scholar

[325] S., Kondō. and I., Shimada. The automorphism group of a supersingular K3 surface with Artin invariant 1 in characteristic 3. Int. Math. Res. Not. IMRN, (7):1885–1924, 2014. (Cited on page 345.)Google Scholar

[326] S., Kondō. and I., Shimada. On a certain duality of Néron–Severi lattices of supersingular K3 surfaces. Algebr. Geom., 1(3):311–333, 2014. (Cited on pages 401, 402, and 403.)Google Scholar

[327] S., Kovács. The cone of curves of a K3 surface. Math. Ann., 300(4):681–691, 1994. (Cited on pages 160, 162, 163, 281, and 316.)Google Scholar

[328] H., Kraft, P., Slodowy, and T., Springer, editors. Algebraische Transformationsgruppen und Invariantentheorie, vol. 13 of DMV Seminar. Birkhäuser Verlag, Basel, 1989. (Cited on page 94.)

[329] A., Kresch. Hodge-theoretic obstruction to the existence of quaternion algebras. Bull. Lond. Math. Soc., 35(1):109–116, 2003. (Cited on page 412.)Google Scholar

[330] A., Kresch. On the geometry of Deligne–Mumford stacks. In Algebraic geometry – Seattle 2005. Part 1, vol. 80 of Proc. Sympos. Pure Math., pages 259–271. Amer. Math. Soc., Providence, RI, 2009. (Cited on page 99.)

[331] M., Kuga and I., Satake. Abelian varieties attached to polarized K3 surfaces. Math. Ann., 169:239–242, 1967. (Cited on page 72.)Google Scholar

[332] S., Kuleshov. A theorem on the existence of exceptional bundles on surfaces of type K3. Izv. Akad. Nauk SSSR Ser. Mat., 53(2):363–378, 1989. (Cited on pages 198 and 212.)Google Scholar

[333] S., Kuleshov. Exceptional bundles on K3 surfaces. In Helices and vector bundles, vol. 148 of Lond. Math. Soc. Lecture Note Ser., pages 105–114. Cambridge University Press, 1990. (Cited on page 198.)

[334] S., Kuleshov. Stable bundles on a K3 surface. Izv. Akad. Nauk SSSR Ser. Mat., 54(1):213–220, 223, 1990. (Cited on page 198.)Google Scholar

[335] V., Kulikov. Degenerations of K3 surfaces and Enriques surfaces. Izv. Akad. Nauk SSSR Ser. Mat., 41(5):1008–1042, 1199, 1977. (Cited on pages 114, 125, and 138.)Google Scholar

[336] V., Kulikov. Surjectivity of the period mapping for K3 surfaces. Uspehi Mat. Nauk, 32(4(196)):257–258, 1977. (Cited on page 127.)Google Scholar

[337] V., Kulikov. Surgery of degenerations of surfaces with κ = 0. Izv. Akad. Nauk SSSR Ser. Mat., 44(5):1115–1119, 1214, 1980. (Cited on page 125.)Google Scholar

[338] V., Kulikov and P., Kurchanov. Complex algebraic varieties: periods of integrals and Hodge structures [MR1060327 (91k:14010)]. In Algebraic geometry, III, vol. 36 of Encyclopaedia Math. Sci., pages 1–217, 263–270. Springer, Berlin, 1998. (Cited on page 126.)

[339] A., Kumar. Elliptic fibrations on a generic Jacobian Kummer surface. J. Algebraic Geom., 23(4):599–667, 2014. (Cited on page 253.)Google Scholar

[340] H., Kurke. Vorlesungen über algebraische Flächen, vol. 43 of Teubner-Texte zur Mathematik. BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1982. (Cited on page 15.)

[341] M., Kuwata. Elliptic fibrations on quartic K3 surfaces with large Picard numbers. Pacific J. Math., 171(1):231–243, 1995. (Cited on pages 253, 389, and 390.)Google Scholar

[342] M., Kuwata. Elliptic K3 surfaces with given Mordell–Weil rank. Comment. Math. University St. Paul., 49(1):91–100, 2000. (Cited on page 237.)Google Scholar

[343] M., Kuwata. Equal sums of sixth powers and quadratic line complexes. Rocky Mountain J. Math., 37(2):497–517, 2007. (Cited on page 390.)Google Scholar

[344] M., Kuwata and T., Shioda. Elliptic parameters and defining equations for elliptic fibrations on a Kummer surface. In Algebraic geometry in East Asia–Hanoi 2005, vol. 50 of Adv. Stud. Pure Math., pages 177–215. Math. Soc. Japan, Tokyo, 2008. (Cited on page 253.)

[345] A., Kuznetsov. Derived categories of cubic fourfolds. In Cohomological and geometric approaches to rationality problems, vol. 282 of Progr. Math., pages 219–243. Birkhäuser, Boston 2010. (Cited on page 384.)

[346] A., Lamari. Courants kählériens et surfaces compactes. Ann. Inst. Fourier (Grenoble), 49(1):vii, x, 263–285, 1999. (Cited on pages 135, 137, and 171.)Google Scholar

[347] A., Lamari. Le cône kählérien d'une surface. J. Math. Pures Appl. (9), 78(3):249–263, 1999. (Cited on page 171.)Google Scholar

[348] S., Lang and A., Néron. Rational points of abelian varieties over function fields. Amer. J. Math., 81:95–118, 1959. (Cited on page 5.)Google Scholar

[349] W., Lang and N., Nygaard. A short proof of the Rudakov–Safarevič theorem. Math. Ann., 251(2):171–173, 1980. (Cited on pages 189 and 194.)Google Scholar

[350] A., Langer and S., Saito. Torsion zero-cycles on the self-product of a modular elliptic curve. Duke Math. J., 85(2):315–357, 1996. (Cited on page 270.)Google Scholar

[351] R., Laza. Triangulations of the sphere and degenerations of K3 surfaces. 2008. arXiv:0809.0937. (Cited on page 126.)

[352] R., Laza. The KSBA compactification for the moduli space of degree two K3 pairs. 2012. arXiv:1205.3144. (Cited on page 127.)

[353] M., Lazard. Sur les groupes de Lie formels à un paramètre. Bull. Soc. Math. France, 83:251–274, 1955. (Cited on page 429.)Google Scholar

[354] R., Lazarsfeld. Brill–Noether–Petri without degenerations. J. Differential Geom., 23(3):299–307, 1986. (Cited on pages 181, 182, and 184.)Google Scholar

[355] R., Lazarsfeld. A sampling of vector bundle techniques in the study of linear series. In Lectures on Riemann surfaces (Trieste, 1987), pages 500–559. World Sci. Publ., Teaneck, NJ, 1989. (Cited on pages 182 and 183.)

[356] R., Lazarsfeld. Lectures on linear series. In Complex algebraic geometry (Park City, UT, 1993), vol. 3 of IAS/Park City Math. Ser., pages 161–219. Amer. Math. Soc., Providence, RI, 1997. With the assistance of Guillermo Fernández del Busto. (Cited on pages 33, 180, and 183.)

[357] R., Lazarsfeld. Positivity in algebraic geometry. I, II, vols. 48, 49 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3). Springer-Verlag, Berlin, 2004. (Cited on pages 24, 33, 34, 149, 158, and 174.)

[358] V., Lazić. Around and beyond the canonical class. In Birational geometry, rational curves, and arithmetic, pages 171–203. Springer-Verlag, New York, 2013. (Cited on page 165.)

[359] M., Lehn. Symplectic moduli spaces. In Intersection theory and moduli, ICTP Lect. Notes, XIX, pages 139–184 (electronic). Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2004. (Cited on page 216.)

[360] J., Li and C., Liedtke. Rational curves on K3 surfaces. Invent. Math., 188(3):713–727, 2012. (Cited on pages 281, 286, 287, 288, 289, 290, 291, and 292.)Google Scholar

[361] Z., Li and Z., Tian. Picard groups of moduli of K3 surfaces of low degree K3 surfaces. 2013. arXiv:1304.3219. (Cited on pages 90 and 127.)

[362] D., Lieberman. Compactness of the Chow scheme: applications to automorphisms and deformations of Kähler manifolds. In Fonctions de plusieurs variables complexes, III (Sém. François Norguet, 1975–1977), vol. 670 of Lecture Notes in Math., pages 140–186. Springer-Verlag, Berlin, 1978. (Cited on page 337.)

[363] D., Lieberman and D., Mumford. Matsusaka's big theorem. In Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974), pages 513–530. Amer. Math. Soc., Providence, RI, 1975. (Cited on page 34.)

[364] M., Lieblich. Groupoids and quotients in algebraic geometry. In Snowbird lectures in algebraic geometry, vol. 388 of Contemp. Math., pages 119–136. Amer. Math. Soc., Providence, RI, 2005. (Cited on page 83.)

[365] M., Lieblich. Moduli of twisted sheaves. Duke Math. J., 138(1):23–118, 2007. (Cited on page 383.)Google Scholar

[366] M., Lieblich. Twisted sheaves and the period-index problem. Compositio Math., 144(1):1–31, 2008. (Cited on page 412.)Google Scholar

[367] M., Lieblich. On the unirationality of supersingular K3 surfaces. 2014. arXiv:1403.3073. (Cited on page 437.)

[368] M., Lieblich. Rational curves in the moduli of supersingular K3 surfaces. 2015. arXiv:1507.08387. (Cited on page 437.)

[369] M., Lieblich and D., Maulik. A note on the cone conjecture for K3 surfaces in positive characteristic. 2011. arXiv:1102.3377v3. (Cited on pages 168, 169, 197, 339, and 340.)

[370] M., Lieblich, D., Maulik, and A., Snowden. Finiteness of K3 surfaces and the Tate conjecture. Ann. Sci. Éc. Norm. Supér. (4), 47(2):285–308, 2014. (Cited on pages 408, 425, and 426.)Google Scholar

[371] M., Lieblich and M., Olsson. Fourier–Mukai partners of K3 surfaces in positive characteristic. 2011. arXiv:1112.5114. (Cited on pages 197, 373, 379, and 380.)

[372] C., Liedtke. Lectures on supersingular K3 surfaces and the crystalline Torelli theorem. 2014. arXiv:1403.2538. (Cited on pages 197, 433, and 437.)

[373] C., Liedtke. Supersingular K3 surfaces are unirational. Invent. Math., 200(3):979–1014, 2015. (Cited on pages 264, 273, 292, and 437.)Google Scholar

[374] C., Liedtke and Y., Matsumoto. Good reduction of K3 surfaces. 2014. arXiv:1411.4797. (Cited on page 127.)

[375] Q., Liu. Algebraic geometry and arithmetic curves, vol. 6 of Oxford Graduate Texts in Mathematics. Oxford University Press, Oxford, 2002. (Cited on pages 1, 2, 219, 222, and 226.)

[376] Q., Liu, D., Lorenzini, and M., Raynaud. On the Brauer group of a surface. Invent. Math., 159(3):673–676, 2005. (Cited on page 423.)Google Scholar

[377] G., Lombardo. Abelian varieties of Weil type and Kuga–Satake varieties. Tohoku Math. J. (2), 53(3):453–466, 2001. (Cited on page 79.)Google Scholar

[378] E., Looijenga. A Torelli theorem for Kähler–Einstein K3 surfaces. In Geometry Symposium, Utrecht 1980, vol. 894 of Lecture Notes in Math., pages 107–112. Springer Verlag, Berlin, 1981. (Cited on pages 115 and 146.)

[379] E., Looijenga. Discrete automorphism groups of convex cones of finite type. Compositio Math., 150(11):1939–1962, 2014. (Cited on page 167.)Google Scholar

[380] E., Looijenga and C., Peters. Torelli theorems for Kähler K3 surfaces. Compositio Math., 42(2):145–186, 1980/1981. (Cited on pages 307, 321, and 324.)Google Scholar

[381] M., Lübke and A., Teleman. The Kobayashi–Hitchin correspondence. World Scientific River Edge, NJ, 1995. (Cited on page 192.)

[382] S., Ma. Fourier–Mukai partners of a K3 surface and the cusps of its Kähler moduli. Internat. J. Math., 20(6):727–750, 2009. (Cited on page 384.)Google Scholar

[383] S., Ma. Twisted Fourier–Mukai number of a K3 surface. Trans. Amer. Math. Soc., 362(1):537–552, 2010. (Cited on page 377.)Google Scholar

[384] N., Machida and K., Oguiso. On K3 surfaces admitting finite non-symplectic group actions. J. Math. Sci. University Tokyo, 5(2):273–297, 1998. (Cited on pages 336 and 356.)Google Scholar

[385] C., Maclean. Chow groups of surfaces with h2,0 ≤ 1. C. R. Math. Acad. Sci. Paris, 338(1):55–58, 2004. (Cited on pages 271, 296, and 297.)Google Scholar

[386] E., Macrì and P., Stellari. Automorphisms and autoequivalences of generic analytic K3 surfaces. J. Geom. Phys., 58(1):133–164, 2008. (Cited on pages 51, 342, 357, and 382.)Google Scholar

[387] K. Madapusi, Pera. The Tate conjecture for K3 surfaces in odd characteristic. Invent. Math., 201(2):625–668, 2015. (Cited on pages 89, 99, 129, 211, and 407.)Google Scholar

[388] Y., Manin. Theory of commutative formal groups over fields of finite characteristic. Uspehi Mat. Nauk, 18(6(114)):3–90, 1963. (Cited on page 430.)Google Scholar

[389] Y., Manin. The Tate height of points on an Abelian variety, its variants and applications. Izv. Akad. Nauk SSSR Ser. Mat., 28:1363–1390, 1964. (Cited on page 237.)Google Scholar

[390] E., Markman and K., Yoshioka. A proof of the Kawamata–Morrison cone conjecture for holomorphic symplectic varieties of K3[n] or generalized Kummer deformation type. 2014. arXiv:1402.2049. (Cited on page 174.)

[391] G., Mason. Symplectic automorphisms of K3 surfaces (after S. Mukai and V. V. Nikulin). CWI Newslett., 13:3–19, 1986. (Cited on pages 344 and 345.)Google Scholar

[392] É., Mathieu. Mémoire sur l'étude des fonctions de plusieurs quantités, sur la manière de les former et sur les substitutions qui les laissent invariables. J. Math. Pures et Appl., 6:241–323, 1961. (Cited on page 345.)Google Scholar

[393] K., Matsuki. Introduction to the Mori program. Universitext. Springer-Verlag, New York, 2002. (Cited on pages 190 and 304.)

[394] K., Matsumoto, T., Sasaki, and M., Yoshida. The monodromy of the period map of a 4 parameter family of K3 surfaces and the hypergeometric function of type (3, 6). Internat. J. Math., 3(1):164, 1992. (Cited on page 73.)Google Scholar

[395] T., Matsusaka. Polarized varieties with a given Hilbert polynomial. Amer. J. Math., 94:1027–1077, 1972. (Cited on page 34.)Google Scholar

[396] T., Matsusaka and D., Mumford. Two fundamental theorems on deformations of polarized varieties. Amer. J. Math., 86:668–684, 1964. (Cited on pages 90 and 380.)Google Scholar

[397] T., Matumoto. On diffeomorphisms of a K3 surface. In Algebraic and topological theories (Kinosaki, 1984), pages 616–621. Kinokuniya, Tokyo, 1986. (Cited on page 142.)

[398] D., Maulik. Supersingular K3 surfaces for large primes. Duke Math. J., 163(13):2357–2425, 2014. With an appendix by A. Snowden. (Cited on pages 89, 99, 127, 407, and 436.)Google Scholar

[399] D., Maulik and R., Pandharipande. Gromov–Witten theory and Noether–Lefschetz theory. In A celebration of algebraic geometry, vol. 18 of Clay Math. Proc., pages 469–507. Amer. Math. Soc., Providence, RI, 2013. (Cited on pages x and 127.)

[400] D., Maulik and B., Poonen. Néron–Severi groups under specialization. Duke Math. J., 161(11):2167–2206, 2012. (Cited on page 400.)Google Scholar

[401] A., Mayer. Families of K3 surfaces. Nagoya Math. J., 48:1–17, 1972. (Cited on page 23.)Google Scholar

[402] B., Mazur. Frobenius and the Hodge filtration. Bull. Amer. Math. Soc., 78:653–667, 1972. (Cited on page 431.)Google Scholar

[403] C., McMullen. Dynamics on K3 surfaces: Salem numbers and Siegel disks. J. Reine Angew. Math., 545:201–233, 2002. (Cited on pages x and 357.)Google Scholar

[404] J., Milne. On a conjecture of Artin and Tate. Ann. of Math. (2), 102(3):517–533, 1975. (Cited on page 423.)Google Scholar

[405] J., Milne. Étale cohomology, vol. 33 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 1980. (Cited on pages 13, 78, 383, 410, 411, 412, and 413.)

[406] J., Milne. Zero cycles on algebraic varieties in nonzero characteristic: Rojtman's theorem. Compositio Math., 47(3):271–287, 1982. (Cited on page 256.)Google Scholar

[407] J., Milne. Abelian varieties. In Arithmetic geometry (Storrs, CT, 1984), pages 103–150. Springer-Verlag, New York, 1986. (Cited on page 3.)

[408] J., Milne. Introduction to Shimura varieties. Course notes, 2004. (Cited on pages 104 and 105.)

[409] J., Milne. Elliptic curves. BookSurge Publishers, Charleston, SC, 2006. (Cited on pages 241 and 245.)

[410] J., Milne. Class field theory. Course notes 4.02, 2013. (Cited on page 420.)

[411] J., Milnor and D., Husemoller. Symmetric bilinear forms, vol. 73 of Ergebnisse der Mathematik und ihrer Grenzgebiete (2). Springer-Verlag, New York, 1973. (Cited on pages 299 and 305.)

[412] J., Milnor and J., Stasheff. Characteristic classes. Princeton University Press, Princeton, NJ, 1974. Annals of Mathematics Studies, No. 76. (Cited on page 12.)

[413] R., Miranda. The moduli of Weierstrass fibrations over P1. Math. Ann., 255(3):379–394, 1981. (Cited on page 226.)Google Scholar

[414] R., Miranda. The basic theory of elliptic surfaces. Dottorato di Ricerca in Matematica. ETS Editrice, Pisa, 1989. (Cited on pages 219, 224, 226, 229, 231, 235, 236, and 238.)

[415] R., Miranda and D., Morrison. The minus one theorem. In The birational geometry of degenerations (Cambridge, MA, 1981), vol. 29 of Progr. Math., pages 173–259. Birkhäuser, Boston, 1983. (Cited on page 126.)

[416] R., Miranda and U., Persson. Configurations of In fibers on elliptic K3 surfaces. Math. Z., 201(3):339–361, 1989. (Cited on pages 226 and 253.)Google Scholar

[417] Y., Miyaoka. Deformations of a morphism along a foliation and applications. In Algebraic geometry, Bowdoin, 1985 (Brunswick, ME, 1985), vol. 46 of Proc. Sympos. Pure Math., pages 245–268. Amer. Math. Soc., Providence, RI, 1987. (Cited on page 188.)

[418] Y., Miyaoka and T., Peternell. Geometry of higher-dimensional algebraic varieties, vol. 26 of DMV Seminar. Birkhäuser, Basel, 1997. (Cited on pages 188, 189, and 190.)

[419] G., Mongardi. Symplectic involutions on deformations of K3[2]. Cent. Eur. J. Math., 10(4):1472–1485, 2012. (Cited on page 357.)Google Scholar

[420] B., Moonen. An introduction to Mumford–Tate groups. www.math.ru.nl/personal/ bmoonen/Lecturenotes/MTGps.pdf. (Cited on page 53.)

[421] B., Moonen and Y., Zarhin. Hodge classes on abelian varieties of low dimension. Math. Ann., 315(4):711–733, 1999. (Cited on page 71.)Google Scholar

[422] S., Mori. On degrees and genera of curves on smooth quartic surfaces in P3. Nagoya Math. J., 96:127–132, 1984. (Cited on page 34.)Google Scholar

[423] S., Mori and S., Mukai. The uniruledness of the moduli space of curves of genus 11. In Algebraic geometry (Tokyo/Kyoto, 1982), vol. 1016 of Lecture Notes in Math., pages 334–353. Springer-Verlag, Berlin, 1983. (Cited on page 277.)

[424] D., Morrison. On K3 surfaces with large Picard number. Invent. Math., 75(1):105–121, 1984. (Cited on pages 72, 315, 316, 321, 353, and 354.)Google Scholar

[425] D., Morrison. The Kuga–Satake variety of an abelian surface. J. Algebra, 92(2):454–476, 1985. (Cited on pages 70 and 72.)Google Scholar

[426] D., Morrison. The geometry of K3 surfaces. www.math.ucsb.edu/∼drm/manuscripts/ cortona.pdf, 1988. Cortona Lectures. (Cited on page 33.)

[427] I., Morrison. Stability of Hilbert points of generic K3 surfaces. Centre de Recerca Matemática Publication, 401, 1999. (Cited on page 82.)Google Scholar

[428] S., Mukai. Symplectic structure of the moduli space of sheaves on an abelian or K3 surface. Invent. Math., 77(1):101–116, 1984. (Cited on pages 205, 207, and 209.)Google Scholar

[429] S., Mukai. On the moduli space of bundles on K3 surfaces. I. In Vector bundles on algebraic varieties (Bombay, 1984), vol. 11 of Tata Inst. Fund. Res. Stud. Math., pages 341–413. Bombay, 1987. (Cited on pages 185, 206, 208, 211, 212, 317, 373, and 384.)

[430] S., Mukai. Finite groups of automorphisms of K3 surfaces and the Mathieu group. Invent. Math., 94(1):183–221, 1988. (Cited on pages 332, 333, 344, 346, and 350.)Google Scholar

[431] S., Mukai. Biregular classification of Fano 3-folds and Fano manifolds of coindex 3. Proc. Nat. Acad. Sci. U.S.A., 86(9):3000–3002, 1989. (Cited on page 14.)Google Scholar

[432] S., Mukai. Curves and Grassmannians. In Algebraic geometry and related topics (Inchon, 1992), Conf. Proc. Lecture Notes Algebraic Geom., I, pages 19–40. International Press, Cambridge, MA, 1993. (Cited on page 14.)

[433] S., Mukai. New developments in the theory of Fano threefolds: vector bundle method and moduli problems [translation of Sugaku 47(1995), no. 2, 125–144; MR1364825 (96m:14059)]. Sugaku Expositions, 15(2):125–150, 2002. (Cited on page 14.)Google Scholar

[434] S., Mukai. An introduction to invariants and moduli, vol. 81 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, 2003. (Cited on page 90.)

[435] S., Mukai. Polarized K3 surfaces of genus thirteen. In Moduli spaces and arithmetic geometry, vol. 45 of Adv. Stud. Pure Math., pages 315–326. Math. Soc. Japan, Tokyo, 2006. (Cited on page 99.)

[436] S., Müller-Stach, E., Viehweg, and K., Zuo. Relative proportionality for subvarieties of moduli spaces of K3 and abelian surfaces. Pure Appl. Math. Q., 5(3, Special Issue: In honor of F. Hirzebruch. Part 2):1161–1199, 2009. (Cited on page 99.)Google Scholar

[437] D., Mumford. Lectures on curves on an algebraic surface. Annals of Mathematics Studies, No. 59. Princeton University Press, Princeton, NJ, 1966. With a section by G. Bergman. (Cited on pages 4 and 15.)

[438] D., Mumford. Pathologies. III. Amer. J. Math., 89:94–104, 1967. (Cited on page 20.)Google Scholar

[439] D., Mumford. Rational equivalence of 0-cycles on surfaces. J. Math. Kyoto University, 9:195–204, 1968. (Cited on pages 256 and 259.)Google Scholar

[440] D., Mumford. Enriques' classification of surfaces in char p. I. In Global Analysis (Papers in Honor of K. Kodaira), pages 325–339. University of Tokyo Press, Tokyo, 1969. (Cited on page 221.)

[441] D., Mumford. Varieties defined by quadratic equations. In Questions on algebraic varieties (C.I.M.E., III Ciclo, Varenna, 1969), pages 29–100. Edizioni Cremonese, Rome, 1970. (Cited on page 24.)

[442] D., Mumford. Algebraic geometry. I. Classics in Mathematics. Springer-Verlag, Berlin, 1995. Complex projective varieties, Reprint of the 1976 edition. (Cited on page 3.)

[443] D., Mumford. Abelian varieties, vol. 5 of Tata Inst. Fund. Res. Stud. Math. Published for the Tata Institute of Fundamental Research, Bombay, 2008. With appendices by C. P. Ramanujam and Y. Manin. (Cited on pages 3, 23, 58, and 414.)Google Scholar

[444] D., Mumford, J., Fogarty, and F., Kirwan. Geometric invariant theory, vol. 34 of Ergebnisse der Mathematik und ihrer Grenzgebiete (2). Springer-Verlag, Berlin, third edition, 1994. (Cited on pages 85, 89, 90, 94, and 201.)

[445] J., Murre. On the motive of an algebraic surface. J. Reine Angew. Math., 409:190–204, 1990. (Cited on page 265.)Google Scholar

[446] A., Neeman. Algebraic and analytic geometry, vol. 345 of Lond. Math. Soc. Lecture Note Series. Cambridge University Press, 2007. (Cited on page 9.)

[447] A., Néron. Modèles minimaux des variétés abéliennes sur les corps locaux et globaux. Inst. Hautes Études Sci. Publ. Math., 21:128, 1964. (Cited on page 225.)Google Scholar

[448] H.-V., Niemeier. Definite quadratische Formen der Dimension 24 und Diskriminante 1. J. Number Theory, 5:142–178, 1973. (Cited on page 325.)Google Scholar

[449] V., Nikulin. On Kummer surfaces. Izv. Akad. Nauk SSSR Ser. Mat., 39(2):278–293, 471, 1975. (Cited on pages 15, 318, 320, and 321.)Google Scholar

[450] V., Nikulin. Finite groups of automorphisms of Kählerian K3 surfaces. Trudy Moskov. Mat. Obshch., 38:75–137, 1979. (Cited on pages 313, 325, 332, 333, 335, 336, 344, 347, 352, 353, and 387.)Google Scholar

[451] V., Nikulin. Integer symmetric bilinear forms and some of their geometric applications. Izv. Akad. Nauk SSSR Ser. Mat., 43(1):111–177, 238, 1979. (Cited on pages 299, 300, 301, 305, 307, 309, 310, 311, and 313.)Google Scholar

[452] V., Nikulin. Quotient-groups of groups of automorphisms of hyperbolic forms of subgroups generated by 2-reflections. Dokl. Akad. Nauk SSSR, 248(6):1307–1309, 1979. (Cited on page 341.)Google Scholar

[453] V., Nikulin. Quotient-groups of groups of automorphisms of hyperbolic forms by subgroups generated by 2-reflections. Algebro-geometric applications. In Current problems in mathematics, Vol. 18, pages 3–114. Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1981. (Cited on pages 341 and 342.)

[454] V., Nikulin. K3 surfaces with a finite group of automorphisms and a Picard group of rank three. Trudy Mat. Inst. Steklov., 165:119–142, 1984. (Cited on pages 173 and 341.)Google Scholar

[455] V., Nikulin. On correspondences between surfaces of K3 type. Izv. Akad. Nauk SSSR Ser. Mat., 51(2):402–411, 448, 1987. (Cited on page 374.)Google Scholar

[456] V., Nikulin. Kählerian K3 surfaces and Niemeier lattices. I. Izv. Ross. Akad. Nauk Ser. Mat., 77(5):109–154, 2013. Also arXiv:1109.2879. (Cited on page 327.)Google Scholar

[457] V., Nikulin. Elliptic fibrations on K3 surfaces. Proc. Edinb. Math. Soc. (2), 57(1):253–267, 2014. (Cited on page 341.)Google Scholar

[458] K., Nishiguchi. Degeneration of K3 surfaces. J. Math. Kyoto University, 28(2):267–300, 1988. (Cited on page 125.)Google Scholar

[459] K., Nishiyama. Examples of Jacobian fibrations on some K3 surfaces whose Mordell–Weil lattices have the maximal rank 18. Comment. Math. University St. Paul., 44(2):219–223, 1995. (Cited on page 238.)Google Scholar

[460] K., Nishiyama. The Jacobian fibrations on some K3 surfaces and their Mordell–Weil groups. Japan. J. Math. (N.S.), 22(2):293–347, 1996. (Cited on page 253.)Google Scholar

[461] K., Nishiyama. The minimal height of Jacobian fibrations on K3 surfaces. Tohoku Math. J. (2), 48(4):501–517, 1996. (Cited on page 238.)Google Scholar

[462] N., Nygaard. A p-adic proof of the nonexistence of vector fields on K3 surfaces. Ann. of Math. (2), 110(3):515–528, 1979. (Cited on pages 189 and 194.)Google Scholar

[463] N., Nygaard. The Tate conjecture for ordinary K3 surfaces over finite fields. Invent. Math., 74(2):213–237, 1983. (Cited on page 407.)Google Scholar

[464] N., Nygaard and A., Ogus. Tate's conjecture for K3 surfaces of finite height. Ann. of Math. (2), 122(3):461–507, 1985. (Cited on page 407.)Google Scholar

[465] K., O'Grady. On the Picard group of the moduli space for K3 surfaces. Duke Math. J., 53(1):117–124, 1986. (Cited on page 127.)Google Scholar

[466] K., O'Grady. The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface. J. Algebraic Geom., 6(4):599–644, 1997. (Cited on pages 216 and 217.)Google Scholar

[467] K., Oguiso. On Jacobian fibrations on the Kummer surfaces of the product of nonisogenous elliptic curves. J. Math. Soc. Japan, 41(4):651–680, 1989. (Cited on page 253.)Google Scholar

[468] K., Oguiso. A note on Z/pZ-actions on K3 surfaces in odd characteristic p. Math. Ann., 286(4):735–752, 1990. (Cited on page 335.)Google Scholar

[469] K., Oguiso. Families of hyperkähler manifolds. 1999. arXiv:math/9911105. (Cited on page 388.)

[470] K., Oguiso. K3 surfaces via almost-primes. Math. Res. Lett., 9(1):47–63, 2002. (Cited on pages 51, 369, and 384.)Google Scholar

[471] K., Oguiso. Local families of K3 surfaces and applications. J. Algebraic Geom., 12(3):405–433, 2003. (Cited on pages 111, 238, and 356.)Google Scholar

[472] K., Oguiso. A characterization of the Fermat quartic K3 surface by means of finite symmetries. Compositio Math., 141(2):404–424, 2005. (Cited on page 345.)Google Scholar

[473] K., Oguiso. Bimeromorphic automorphism groups of non-projective hyperkähler manifolds – a note inspired by C. T. McMullen. J. Differential Geom., 78(1):163–191, 2008. (Cited on pages 340 and 357.)Google Scholar

[474] K., Oguiso. Free automorphisms of positive entropy on smooth Kähler surfaces. 2012. arXiv:1202.2637. (Cited on page 343.)

[475] K., Oguiso. Some aspects of explicit birational geometry inspired by complex dynamics. 2014. 1404.2982. (Cited on page 357.)

[476] K., Oguiso and T., Shioda. The Mordell–Weil lattice of a rational elliptic surface. Comment. Math. University St. Paul., 40(1):83–99, 1991. (Cited on page 235.)Google Scholar

[477] K., Oguiso and D.-Q., Zhang. On Vorontsov's theorem on K3 surfaces with non-symplectic group actions. Proc. Amer. Math. Soc., 128(6):1571–1580, 2000. (Cited on pages 336 and 337.)Google Scholar

[478] A., Ogus. Supersingular K3 crystals. In: Journées de Géométrie Algébrique de Rennes (Rennes, 1978), Vol. II. Astérisque, 64:3–86, 1979. (Cited on pages 91, 197, 338, 391, 402, 403, and 437.)Google Scholar

[479] A., Ogus. A crystalline Torelli theorem for supersingular K3 surfaces. In Arithmetic and geometry, Vol. II, vol. 36 of Progr. Math., pages 361–394. Birkhäuser, Boston, 1983. (Cited on pages 152, 153, 168, 338, 403, and 437.)

[480] A., Ogus. Singularities of the height strata in the moduli of K3 surfaces. In Moduli of abelian varieties (Texel Island, 1999), vol. 195 of Progr. Math., pages 325–343. Birkhäuser,Basel, 2001. (Cited on page 435.)

[481] M., Olsson. Semistable degenerations and period spaces for polarized K3 surfaces. Duke Math. J., 125(1):121–203, 2004. (Cited on pages 99 and 127.)Google Scholar

[482] N., Onishi and K., Yoshioka. Singularities on the 2-dimensional moduli spaces of stable sheaves on K3 surfaces. Internat. J. Math., 14(8):837–864, 2003. (Cited on page 217.)Google Scholar

[483] D., Orlov. Equivalences of derived categories and K3 surfaces. J. Math. Sci. (New York), 84(5):1361–1381, 1997. Algebraic geometry, 7. (Cited on page 371.)Google Scholar

[484] J., Ottem. Cox rings of K3 surfaces with Picard number 2. J. Pure Appl. Algebra, 217(4):709–715, 2013. (Cited on page 174.)Google Scholar

[485] R., Pandharipande. Maps, sheaves, and K3 surfaces. 2008. arXiv:0808.0253. (Cited on page 297.)

[486] K., Paranjape. Abelian varieties associated to certain K3 surfaces. Compositio Math., 68(1):11–22, 1988. (Cited on page 73.)Google Scholar

[487] K., Paranjape and S., Ramanan. On the canonical ring of a curve. In Algebraic geometry and commutative algebra, Vol. II, pages 503–516. Kinokuniya, Tokyo, 1988. (Cited on page 187.)

[488] G., Pareschi. A proof of Lazarsfeld's theorem on curves on K3 surfaces. J. Algebraic Geom., 4(1):195–200, 1995. (Cited on page 184.)Google Scholar

[489] C., Pedrini. The Chow motive of a K3 surface. Milan J. Math., 77:151–170, 2009. (Cited on page 271.)Google Scholar

[490] U., Persson. On degenerations of algebraic surfaces. Mem. Amer. Math. Soc., 11(189):xv+144, 1977. (Cited on page 125.)

[491] U., Persson. Double sextics and singular K3 surfaces. In Algebraic geometry, Sitges (Barcelona), 1983, vol. 1124 of Lecture Notes in Math., pages 262–328. Springer Verlag, Berlin, 1985. (Cited on pages 234, 329, and 390.)

[492] U., Persson and H., Pinkham. Degeneration of surfaces with trivial canonical bundle. Ann. of Math. (2), 113(1):45–66, 1981. (Cited on pages 114 and 125.)Google Scholar

[493] I., Pjateckiı-Šapiro and I., Šafarevič. Torelli's theorem for algebraic surfaces of type K3. Izv. Akad. Nauk SSSR Ser. Mat., 35:530–572, 1971. (Cited on pages 44, 48, 82, 109, 116, 117, 145, 169, 170, 307, 318, 319, 324, 337, 340, 341, and 343.)Google Scholar

[494] I., Pjateckiı-Šapiro and I., Šafarevič. The arithmetic of surfaces of type K3. In Proc. Internat. Conference on Number Theory (Moscow, 1971), vol. 132, pages 44–54, 1973. English translation in: Proc. of the Steklov Institute of Mathematics, No. 132 (1973), pages 45–57. Amer. Math. Soc., Providence, RI, 1975. (Cited on pages 52, 54, 69, 74, 117, 118, 121, and 143.)Google Scholar

[495] B., Poonen. Rational points on varieties. Course notes, 2013. (Cited on page 410.)

[496] H., Popp. On moduli of algebraic varieties. I. Invent. Math., 22:1–40, 1973/1974. (Cited on page 83.)Google Scholar

[497] H., Popp. On moduli of algebraic varieties. II. Compositio Math., 28:51–81, 1974. (Cited on page 83.)Google Scholar

[498] H., Popp. On moduli of algebraic varieties. III. Fine moduli spaces. Compositio Math., 31(3):237–258, 1975. (Cited on page 83.)Google Scholar

[499] A., Prendergast-Smith. The cone conjecture for abelian varieties. J. Math. Sci. University Tokyo, 19(2):243–261, 2012. (Cited on page 167.)Google Scholar

[500] C., Procesi. Lie groups. Universitext. Springer-Verlag, New York, 2007. (Cited on pages 59, 61, and 142.)

[501] S., Rams and M., Schütt. 64 lines on smooth quartic surfaces. Math. Ann., 362(1–2): 679–698, 2015. (Cited on page 297.)Google Scholar

[502] S., Rams and T., Szemberg. Simultaneous generation of jets on K3 surfaces. Arch. Math. (Basel), 83(4):353–359, 2004. (Cited on page 33.)Google Scholar

[503] Z., Ran. Hodge theory and deformations of maps. Compositio Math., 97(3):309–328, 1995. (Cited on page 286.)Google Scholar

[504] M., Rapoport, N., Schappacher, and P., Schneider, editors. Beilinson's conjectures on special values of L-functions, vol. 4 of Perspectives in Mathematics. Academic Press, Boston, 1988. (Cited on page 261.)

[505] W., Raskind. Torsion algebraic cycles on varieties over local fields. In Algebraic K-theory: connections with geometry and topology (Lake Louise, AB, 1987), vol. 279 of NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., pages 343–388. Kluwer Academic, Dordrecht, 1989. (Cited on page 270.)

[506] M., Raynaud. Contre-exemple au “vanishing theorem” en caractéristique p > 0. In C. P. Ramanujam – a tribute, vol. 8 of Tata Inst. Fund. Res. Stud. Math., pages 273–278. Springer-Verlag, Berlin, 1978. (Cited on page 20.)

[507] M., Raynaud. Faisceaux amples et très amples [d'après T. Matsusaka], Séminaire Bourbaki, Exposé 493, 1976/1977, vol. 677 of Lecture Notes in Math., pages 46–58. Springer Verlag, Berlin, 1978. (Cited on page 34.)

[508] M., Raynaud. “p-torsion” du schéma de Picard. In Journées de Géométrie Algébrique de Rennes (Rennes, 1978), Vol. II, vol. 64 of Astérisque, pages 87–148. Soc. Math. France, Paris, 1979. (Cited on page 397.)

[509] M., Reid. Chapters on algebraic surfaces. In Complex algebraic geometry (Park City, UT, 1993), vol. 3 of IAS/Park City Math. Ser., pages 3–159. Amer. Math. Soc., Providence, RI, 1997. (Cited on pages 15, 18, 21, 28, and 33.)

[510] J., Rizov. Moduli stacks of polarized K3 surfaces in mixed characteristic. Serdica Math. J., 32(2-3):131–178, 2006. (Cited on pages 84, 91, 92, 98, 333, and 338.)Google Scholar