Moduli of twisted sheaves
By Max Lieblich. 2004
172 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fbc625e85f4d78431a786e3e103a8abee9d077f6
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In Geometry and Topology
- Max Lieblich
- A. Langer
- D. Huybrechts
- Emanuele Macrì
- Yukinobu Toda
- P. Stellari
- Bertrand Toën
- Arend Bayer
In Mathematical Physics
- Max Lieblich
- A. Langer
- D. Huybrechts
- Emanuele Macrì
- Yukinobu Toda
- P. Stellari
- Bertrand Toën
- Arend Bayer
Citations in the corpus
- Period and index in the Brauer group of an arithmetic surface (2007, background): “For basic results on gerbes, the reader is referred to [11] or, for a condensed discussion, [26] or [24].”
- Projectivity and birational geometry of Bridgeland moduli spaces (2012, unknown): “Moduli of β -twisted ω -Gieseker semistable α -twisted sheaves share the same properties as untwisted sheaves (see [50, 84]).”
- Lectures on K3 Surfaces (2016, unknown): “The gerbeM{αijk} associates with T //X the categoryM{αijk}(T ) whose objects are collections {Li, φij}, where Li ∈ Pic(TUi) and φij : Lj |TUij ∼ − // Li|TUij with φij ·φjk ·φki = αijk, see [363].”
- Moduli spaces of sheaves and principal G-bundles (2009, methodology): “Lieblich in [44] used twisted sheaves to construct a moduli stack of semista ble PGLnbundles on surfaces if n does not divide the characteristic of the base field.”