Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences

N. Addington, W. Donovan, C. Meachan

Published 2015-07-09Version 1

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 Kawamata's "K-equivalence implies D-equivalence" conjecture for moduli spaces of sheaves on K3 surfaces.