15 May 2007 Moduli of twisted sheaves
Max Lieblich
Author Affiliations +
Duke Math. J. 138(1): 23-118 (15 May 2007). DOI: 10.1215/S0012-7094-07-13812-2

Abstract

We study moduli of semistable twisted sheaves on smooth proper algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to spaces of semistable vector bundles. In the case of surfaces, we show (under a mild hypothesis on the twisting class) that the spaces are asymptotically geometrically irreducible, normal, generically smooth, and locally complete intersections (l.c.i.'s) over the base. We also develop general tools necessary for these results: the theory of associated points and purity of sheaves on Artin stacks, twisted Bogomolov inequalities, semistability and boundedness results, and basic results on twisted Quot-schemes on a surface

Citation

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Max Lieblich. "Moduli of twisted sheaves." Duke Math. J. 138 (1) 23 - 118, 15 May 2007. https://doi.org/10.1215/S0012-7094-07-13812-2

Information

Published: 15 May 2007
First available in Project Euclid: 9 May 2007

zbMATH: 1122.14012
MathSciNet: MR2309155
Digital Object Identifier: 10.1215/S0012-7094-07-13812-2

Subjects:
Primary: 14D20

Rights: Copyright © 2007 Duke University Press

Vol.138 • No. 1 • 15 May 2007
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