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On the moduli of stable sheaves on a reducible projective scheme and examples on a reducible quadric surface

Published online by Cambridge University Press:  22 January 2016

Michi-Aki Inaba
Michi-Aki Inaba*
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan, inaba@kusm.kyoto-u.ac.jp
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Abstract

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We study the moduli space of stable sheaves on a reducible projective scheme by use of a suitable stratification of the moduli space. Each stratum is the moduli space of “triples”, which is the main object investigated in this paper. As an application, we can see that the relative moduli space of rank two stable sheaves on quadric surfaces gives a nontrivial example of the relative moduli space which is not flat over the base space.

Keywords

14D2014D0614J60

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 166 , June 2002 , pp. 135 - 181
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[1] Altman, A. and Kleiman, S., Compactifying the Picard scheme, Adv. in Math., 35 (1980), no. 1, 50–112.CrossRefGoogle Scholar
[2] Faltings, G., Moduli-stacks for bundles on semistable curves, Math. Ann., 304 (1996), 489–515.CrossRefGoogle Scholar
[3] Gieseker, D. and Li, J., Irreducibility of moduli of rank-2 vector bundles on Algebraic surfaces, J. Differential Geom., 40 (1994), 23–104.CrossRefGoogle Scholar
[4] Grothendieck, A., Eléments de géométrie algébrique, Chaps. I,II,III,IV, Inst. Hautes Etudes Sci. Publ. Math. No. 4,8,11,17,20,24,28,32, 1960–1967.Google Scholar
[5] Inaba, M., Moduli of parabolic stable sheaves on a projective scheme, J. Math. Kyoto Univ., 40–1 (2000), 119–136.Google Scholar
[6] Inaba, M., On the moduli of stable sheaves on some nonreduced projective schemes, (to appear in J. Alg. Geometry).CrossRefGoogle Scholar
[7] Langer, A., Semistable sheaves in positive characteristic, (to appear).CrossRefGoogle Scholar
[8] Maruyama, M., Moduli of stable sheaves, II, J. Math. Kyoto Univ., 18 (1978), no. 3, 557–614.Google Scholar
[9] Maruyama, M., Construction of moduli spaces of stable sheaves via Simpson’s idea, Lecture Notes in Pure and Appl. Math. 179, Dekker, New York, (1996).Google Scholar
[10] Mumford, D., Geometric invariant theory, Springer-Verlag, Berlin Heidelberg New York, 1965.CrossRefGoogle Scholar
[11] Nagaraj, D. S. and Seshadri, C. S., Degenerations of the moduli spaces of vector bundles on curves, I, Proc. Indian Acad. Sci., 107 (1997), no. 2, 101–137.Google Scholar
[12] Oda, T. and Seshadri, C. S., Compactification of the generalized Jacobian variety, Trans. Amer. Math. Soc, 253 (1979), 1–90.CrossRefGoogle Scholar
[13] Okonek, C., Schneider, M., Spindler, H., Vector bundles on complex projective spaces, Birkhäuser, Boston, 1980.Google Scholar
[14] Rudakov, A. N., A description of Chern classes of semistable sheaves on a quadric surface, J. Reine Angew. Math., 453 (1994), 113–135.Google Scholar
[15] Seshadri, C. S., Geometric reductivity over arbitrary base, Adv. in Math., 26 (1977), no. 3, 225–274.CrossRefGoogle Scholar
[16] Seshadri, C. S., Fibres vectoriels sur les courbes algébriques, Astérisque, 96, Société Mathématique de France, Paris, 1982.Google Scholar
[17] Simpson, C. T., Moduli of representations of the fundamental group of a smooth projective variety I, Inst. Hautes Etudes Sci., 79 (1994), 47–129.CrossRefGoogle Scholar
[18] Soberon-Chavez, S., Rank 2 vector bundles over a complex quadric surface, Quart. J. Math. Oxford (2), 36 (1985), 159–172.CrossRefGoogle Scholar
[19] Yokogawa, K., Compactification of moduli of parabolic sheaves and moduli of parabolic Higgs sheaves, J. Math. Kyoto Univ., 33 (1993), no. 2, 451–504.Google Scholar
[20] Xia, H., Degenerations of moduli of stable bundles over algebraic curves, Compos. Math., 98 (1995), 305–330.Google Scholar