Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences

Abstract

We show that for many moduli spaces M of torsion sheaves on K3 surfaces S, the functor D(S) -> D(M) induced by the universal sheaf is a P-functor, hence can be used to construct an autoequivalence of D(M), and that this autoequivalence can be factored into geometrically meaningful equivalences associated to abelian fibrations and Mukai flops. Along the way we produce a derived equivalence between two compact hyperkaehler 2g-folds that are not birational, for every g >= 2. We also speculate about an approach to showing that birational moduli spaces of sheaves on K3 surfaces are derived-equivalent.

28 pages. typos corrected. final version to appear in JLMS

References in corpus (1)

• Integral Transforms and Deformations of K3 Surfaces

Cited by in corpus (10)

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• Stable vector bundles on generalized Kummer varieties
• A categorical sl_2 action on some moduli spaces of sheaves
• Stability of some vector bundles on Hilbert schemes of points on K3 surfaces
• Universal functors on symmetric quotient stacks of Abelian varieties
• Towards a modular construction of OG10
• Stability and certain ${\mathbb{P}}^n$-functors