Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences

Addington, N., Donovan, W. and Meachan, C. (2016) Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences. Journal of the London Mathematical Society, 93(3), pp. 846-865. (doi: 10.1112/jlms/jdw022)

Abstract

We show that for many moduli spaces M of torsion sheaves on K3 surfaces S, the functor Db (S) → Db (M) induced by the universal sheaf is a P-functor, hence can be used to construct an autoequivalence of Db (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 hyperk¨ahler 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.

• Item Type: Articles
• Additional Information: The first author was partially supported by NSF grant no. DMS–0905923. The second author was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan; and by EPSRC grant EP/G007632/1. The third author was supported by the EPSRC Doctoral Prize Research Fellowship Grant EP/K503034/1.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Meachan, Dr Ciaran
• Authors: Addington, N., Donovan, W., and Meachan, C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of the London Mathematical Society
• Publisher: Cambridge University Press
• ISSN: 0024-6107
• ISSN (Online): 1469-7750
• Published Online: 13 May 2016
• Copyright Holders: Copyright © 2016 The Authors
• First Published: First published in Journal of the London Mathematical Society 93(3): 846-865
• Publisher Policy: Reproduced in accordance with the publisher copyright policy