Moduli of twisted sheaves

Details Moduli of twisted sheaves Moduli of twisted sheaves

2004-11-15

arxiv.org/abs/math/0411337v2

Mathematics

Algebraic Geometry

65 pages, minor changes made and typographical errors corrected

Scientific paper

We study moduli of semistable twisted sheaves on smooth proper morphisms of 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 asympotically geometrically irreducible, normal, generically smooth, and l.c.i. 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.

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