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On the moduli of stable sheaves on some nonreduced projective schemes
Author(s):
Michi-aki
Inaba
Journal:
J. Algebraic Geom.
13
(2004),
1-27.
Posted:
August 26, 2003
MathSciNet review:
2008714
Retrieve article in:
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Abstract |
References |
Additional information
Abstract:
We study the moduli space of stable sheaves on a projective scheme whose structure sheaf has a nilpotent ideal with some property. We introduce a stratification on this moduli space. Each stratum is the moduli space of some extensions of sheaves. This stratification is described on a curve with multiple structure and on a double plane, and the structure of each stratum is studied. In the case of a curve with multiple structure, we also study a local structure of the moduli space of stable sheaves.
References:
-
- 1.
- A. Altman and S. Kleiman, Compactifying the Picard scheme, Adv. in Math. 35 (1980), no. 1, 50-112.
- 2.
- G. Faltings, Moduli-stacks for bundles on semistable curves, Math. Ann. 304 (1996) 489-515.
- 3.
- D. Gieseker and J. Li, Irreducibility of moduli of rank-
 vector bundles on algebraic surfaces, J. Differential Geometry 40 (1994), 23-104. - 4.
- A. Grothendieck, Éléments de géométrie algébrique, Chaps. I,II,III,IV, Inst. Hautes Études Sci. Publ. Math. Nos. 4,8,11,17,20,24,28,32 (1960-1967).
- 5.
- M. Inaba, On the moduli of stable sheaves on a reducible projective scheme and examples on a reducible quadric surface, Nagoya Math. J. 166 (2002), 135-181.
- 6.
- T. Kawai and K. Yoshioka, String partition functions and infinite products, Adv. Theor. Math. Phys. 4 (2000), no. 2, 397-485.
- 7.
- H. Lange, Universal families of extensions, J. Algebra 83 (1983), 101-112.
- 8.
- A. Langer, Semistable sheaves in positive characteristic, (to appear).
- 9.
- J. Le Potier, Faisceaux semi-stables de dimension 1 sur le plan projectif, Rev. Roumaine Math. Pures Appl. 38 (1993) no. 7-8, 635-678.
- 10.
- J. Le Potier, Faisceaux semi-stables et systèmes cohérents, Vector bundles in algebraic geometry, 179-239, London Math. Soc. Lecture Note Ser. 208, Cambridge Univ. Press, Cambridge, (1995).
- 11.
- J. Le Potier, Systèmes cohérents et structures de niveau, Asterisque 214 (1993).
- 12.
- M. Maruyama, Moduli of stable sheaves, II, J. Math. Kyoto Univ. 18 (1978), no. 3, 557-614.
- 13.
- M. Maruyama, Construction of moduli spaces of stable sheaves via Simpson's idea, Lecture Notes in Pure and Appl. Math. 179. Dekker, New York, (1996).
- 14.
- D. Mumford, Geometric invariant theory, Springer-Verlag, Berlin Heidelberg New York (1965).
- 15.
- D. Mumford, Lectures on curves on an algebraic surface, Annals of Math. Studies No. 59, Princeton Univ. Press, (1966).
- 16.
- D. S. Nagaraj and C. S. Seshadri, Degenerations of the moduli spaces of vector bundles on curves I, Proc. Indian Acad. Sci. 107 (1997), no. 2, 101-137.
- 17.
- T. Nüßler and G. Trautmann, Multiple Koszul structres on lines and instanton bundles, Internat. J. Math. 5 (1994), no. 3, 373-388.
- 18.
- T. Oda and C. S. Seshadri, Compactification of the generalized Jacobian variety. Trans. Am. Math. Soc. 253 (1979) 1-90.
- 19.
- C. Okonek, M. Schneider and H. Spindler, Vector bundles on complex projective spaces, Birkhäuser, Boston (1980).
- 20.
- C. S. Seshadri, Geometric reductivity over arbitrary base, Advances in Math. 26 (1977), no. 3, 225-274.
- 21.
- C. S. Seshadri, Fibrés vectoriels sur les courbes algébriques, Asterisque 96. Société Mathématique de France, Paris, (1982).
- 22.
- C. T. Simpson, Moduli of representations of the fundamental group of a smooth projective variety I, Inst. Hautes Études Sci Publ. Math. No. 79 (1994), 47-129.
- 23.
- S. Soberon-Chavez, Rank
 vector bundles over a complex quadric surface, Quart. J. Math. Oxford Ser. (2), 36 (1985), 159-172. - 24.
- H. Xia, Degenerations of moduli of stable bundles over algebraic curves, Compos. Math. 98 (1995) 305-330.
Additional Information:
Michi-aki
Inaba
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan
Address at time of publication:
Graduate School of Mathematics, Kyushu University 33, Fukuoka 812-8581, Japan
Email:
inaba@kusm.kyoto-u.ac.jp, inaba@math.kyushu-u.ac.jp
DOI:
10.1090/S1056-3911-03-00333-3
PII:
S 1056-3911(03)00333-3
Received by editor(s):
June 27, 2000
Received by editor(s) in revised form:
October 21, 2001
Posted:
August 26, 2003
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