Download this article
 Download this article For screen
For printing
Recent Issues

Volume 28
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Derived equivalences of hyperkähler varieties

Lenny Taelman

Geometry & Topology 27 (2023) 2649–2693
Abstract

We show that the Looijenga–Lunts–Verbitsky Lie algebra acting on the cohomology of a hyperkähler variety is a derived invariant, and obtain from this a number of consequences for the action on cohomology of derived equivalences between hyperkähler varieties.

This includes a proof that derived equivalent hyperkähler varieties have isomorphic –Hodge structures, the construction of a rational “Mukai lattice” functorial for derived equivalences, and the computation (up to index 2) of the image of the group of auto-equivalences on the cohomology of certain Hilbert squares of K 3 surfaces.

Keywords
hyperkähler varieties, derived equivalences, Fourier–Mukai transforms
Mathematical Subject Classification 2010
Primary: 14F05, 14J32
References
Publication
Received: 17 March 2020
Revised: 2 November 2021
Accepted: 15 January 2022
Published: 19 September 2023
Proposed: Richard P Thomas
Seconded: Jim Bryan, Dan Abramovich
Authors
Lenny Taelman
Korteweg-de Vries Institute for Mathematics
University of Amsterdam
Amsterdam
Netherlands

Open Access made possible by participating institutions via Subscribe to Open.