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On the components of moduli of simple sheaves on a surface

On the components of moduli of simple sheaves on a surface Abstract. Here we give several constructions of moduli schemes of simple vector bundles and simple sheaves with fixed Chern classes on an algebraic surface with infinitely many irreducible components. 1991 Mathematics Subject Classification: 14J60, 14F05, 14D20. Recently in [Q] Z. Qin gave a quite complete picture of the moduli schemes of rank 2 simple torsion free sheaves on an elliptic K3 surface S. In particular he proved exactly ([Q], th. C) for which S (the one with rank(Pic(,S)) > 2) and which Chern classes the "moduli scheme" of rank 2 simple sheaves has infinitely many components. The aim of this paper is to show that for other surfaces (in particular for most non minimal ones) it is quite common the existence of infinitely many irreducible components in the "moduli schemes" for simple sheaves with fixed Chern classes (and even for simple bundles, a possibility which never arises in the case analized in [Q]). An equivalent formulation of "infinitely many irreducible components" would be "the set of all such object is not bounded" where "bounded" means "there is no algebraic variety whose closed points paramefrize all these objects and possibly several other ones" (see for instance [K] or [M] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

On the components of moduli of simple sheaves on a surface

Forum Mathematicum , Volume 6 (6) – Jan 1, 1994

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1994.6.35
Publisher site
See Article on Publisher Site

Abstract

Abstract. Here we give several constructions of moduli schemes of simple vector bundles and simple sheaves with fixed Chern classes on an algebraic surface with infinitely many irreducible components. 1991 Mathematics Subject Classification: 14J60, 14F05, 14D20. Recently in [Q] Z. Qin gave a quite complete picture of the moduli schemes of rank 2 simple torsion free sheaves on an elliptic K3 surface S. In particular he proved exactly ([Q], th. C) for which S (the one with rank(Pic(,S)) > 2) and which Chern classes the "moduli scheme" of rank 2 simple sheaves has infinitely many components. The aim of this paper is to show that for other surfaces (in particular for most non minimal ones) it is quite common the existence of infinitely many irreducible components in the "moduli schemes" for simple sheaves with fixed Chern classes (and even for simple bundles, a possibility which never arises in the case analized in [Q]). An equivalent formulation of "infinitely many irreducible components" would be "the set of all such object is not bounded" where "bounded" means "there is no algebraic variety whose closed points paramefrize all these objects and possibly several other ones" (see for instance [K] or [M]

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 1994

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