Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- 1 The effect of points fattening in dimension three
- 2 Some remarks on surface moduli and determinants
- 3 Valuation spaces and multiplier ideals on singular varieties
- 4 Line arrangements modeling curves of high degree: Equations, syzygies, and secants
- 5 Rationally connected manifolds and semipositivity of the Ricci curvature
- 6 Subcanonical graded rings which are not Cohen–Macaulay
- 7 Threefold divisorial contractions to singularities of cE type
- 8 Special prime Fano fourfolds of degree 10 and index 2
- 9 Configuration spaces of complex and real spheres
- 10 Twenty points in ℙ3
- 11 The Betti table of a high-degree curve is asymptotically pure
- 12 Partial positivity: Geometry and cohomology of q-ample line bundles
- 13 Generic vanishing fails for singular varieties and in characteristic p > 0
- 14 Deformations of elliptic Calabi–Yau manifolds
- 15 Derived equivalence and non-vanishing loci II
- 16 The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces
- 17 Lower-order asymptotics for Szegö and Toeplitz kernels under Hamiltonian circle actions
- 18 Gaussian maps and generic vanishing I: Subvarieties of abelian varieties
- 19 Torsion points on cohomology support loci: From D-modules to Simpson's theorem
- 20 Rational equivalence of 0-cycles on K3 surfaces and conjectures of Huybrechts and O'Grady
- References
5 - Rationally connected manifolds and semipositivity of the Ricci curvature
Published online by Cambridge University Press: 05 January 2015
Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- 1 The effect of points fattening in dimension three
- 2 Some remarks on surface moduli and determinants
- 3 Valuation spaces and multiplier ideals on singular varieties
- 4 Line arrangements modeling curves of high degree: Equations, syzygies, and secants
- 5 Rationally connected manifolds and semipositivity of the Ricci curvature
- 6 Subcanonical graded rings which are not Cohen–Macaulay
- 7 Threefold divisorial contractions to singularities of cE type
- 8 Special prime Fano fourfolds of degree 10 and index 2
- 9 Configuration spaces of complex and real spheres
- 10 Twenty points in ℙ3
- 11 The Betti table of a high-degree curve is asymptotically pure
- 12 Partial positivity: Geometry and cohomology of q-ample line bundles
- 13 Generic vanishing fails for singular varieties and in characteristic p > 0
- 14 Deformations of elliptic Calabi–Yau manifolds
- 15 Derived equivalence and non-vanishing loci II
- 16 The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces
- 17 Lower-order asymptotics for Szegö and Toeplitz kernels under Hamiltonian circle actions
- 18 Gaussian maps and generic vanishing I: Subvarieties of abelian varieties
- 19 Torsion points on cohomology support loci: From D-modules to Simpson's theorem
- 20 Rational equivalence of 0-cycles on K3 surfaces and conjectures of Huybrechts and O'Grady
- References
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Recent Advances in Algebraic GeometryA Volume in Honor of Rob Lazarsfeld’s 60th Birthday, pp. 71 - 91Publisher: Cambridge University PressPrint publication year: 2015
References
[Aro57] A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pures Appl. 36, 235–249 (1957).Google Scholar
[Aub76] Equations du type Monge–Ampère sur les variétés kähleriennes compactes. C. R. Acad. Sci. Paris Ser. A 283, 119–121 (1976); Bull. Sci. Math. 102, 63–95 (1978).Google Scholar
[Bea83] Variétés kähleriennes dont la première classe de Chern est nulle. J. Diff. Geom. 18, 775–782 (1983).Google Scholar
[Ber55] Sur les groupes d'holonomie des variétés à connexion affine des variétés riemanniennes. Bull. Soc. Math. France 83, 279–330 (1955).Google Scholar
[BY53] and Curvature and Betti numbers. Annals of Mathematics Studies, No. 32. Princeton, NJ: Princeton University Press, 1953.
[Bog74a] On the decomposition of Kähler manifolds with trivial canonical class. Math. USSR Sbornik 22, 580–583 (1974).Google Scholar
[Bog74b] Kähler manifolds with trivial canonical class. Izvestija Akad. Nauk 38, 11–21 (1974).Google Scholar
[BDPP] , , , and The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension. J. Alg. Geom. 22, 201–248 (2013).Google Scholar
[Bru10] On Kähler surfaces with semipositive Ricci curvature.Riv. Math. Univ. Parma (N.S.), 1, 441–150 (2010).Google Scholar
[Cam92] Connexité rationnelle des variétés de Fano. Ann. Sci. Ec. Norm. Sup. 25, 539–545 (1992).Google Scholar
[CPZ03] , , and On the Albanese maps of compact Kähler manifolds. Proc. Amer. Math. Soc. 131, 549–553 (2003).Google Scholar
[CG71] and The splitting theorem for manifolds of nonnegative Ricci curvature. J. Diff. Geom. 6, 119–128 (1971).Google Scholar
[CG72] and On the structure of complete manifolds of nonnegative curvature. Ann. Math. 96, 413–443 (1972).Google Scholar
[DPS94] , , and Compact complex manifolds with numerically effective tangent bundles. J. Alg. Geom. 3, 295–345 (1994).Google Scholar
[DPS96] , , and Compact Kähler manifolds with hermitian semipositive anticanonical bundle. Compos. Math. 101, 217–224 (1996).Google Scholar
[DR52] Sur la reductibilité d'un espace de Riemann. Comment. Math. Helv. 26, 328–344 (1952).Google Scholar
[Gau77] Le théorème de l'excentricité nulle. C. R. Acad. Sci. Paris 285, 387–390 (1977).Google Scholar
[GHS01] , , and Families of rationally connected varieties. J. Amer. Math. Soc. 16, 57–67 (2003).Google Scholar
[Kob81] Recent results in complex differential geometry. Jber. dt. Math.-Verein. 83, 147–158 (1981).Google Scholar
[Kob83] Topics in complex differential geometry. In DMV Seminar, Vol. 3. Berlin: Birkhauser, 1983.
[Kol96] Rational Curves on Algebraic Varieties. Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 32. Berlin: Springer-Verlag, 1996.
[Lic67] Variétés Kähleriennes et première classe de Chern. J. Diff. Geom. 1, 195–224 (1967).Google Scholar
[Lic71] Variétés Kählériennes à première classe de Chern non négative et variétés riemanniennes à courbure de Ricci généralisée non négative. J. Diff. Geom. 6, 47–94 (1971).Google Scholar
[Pau12] Relative adjoint transcendental classes and the Albanese map of compact Kähler manifolds with nef Ricci classes. arXiv: 1209.2195.
[Ued82] On the neighborhood of a compact complex curve with topologically trivial normal bundle. J. Math. Kyoto Univ. 22, 583–607 (1982/83).Google Scholar
[Yau78] On the Ricci curvature of a complex Kähler manifold and the complex Monge–Ampère equation I. Comm. Pure Appl. Math. 31, 339–411 (1978).Google Scholar
[Zha96] On projective manifolds with nef anticanonical bundles. J. Reine Angew. Math. 478, 57–60 (1996).Google Scholar
[Zha05] On projective varieties with nef anticanonical divisors. Math. Ann. 332, 697–703 (2005).Google Scholar
- 6
- Cited by