Moduli Spaces of Sheaves on K3 Surfaces and Symplectic Stacks

Details Moduli Spaces of Sheaves on K3 Surfaces and Symplectic Stacks Moduli Spaces of Sheaves on K3 Surfaces and Symplectic Stacks

2011-11-27

arxiv.org/abs/1111.6294v1

Mathematics

Algebraic Geometry

36 pages

Scientific paper

We view the moduli space of semistable sheaves on a K3 surface as a global
quotient stack, and compute its cotangent complex in terms of the universal
sheaf on the Quot scheme. Relevant facts on the classical and reduced Atiyah
classes are reviewed. We also define the notion of a symplectic stack, and show
that it includes all moduli stacks of semistable sheaves on K3 surfaces.

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