Derived equivalences of hyperk\"ahler varieties
Algebraic Geometry
2023-09-27 v5
Abstract
We show that the Looijenga--Lunts--Verbitsky Lie algebra acting on the cohomology of a hyperk\"ahler variety is a derived invariant, and obtain from this a number of consequences for the action on cohomology of derived equivalences between hyperk\"ahler varieties. This includes a proof that derived equivalent hyperk\"ahler 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 K3 surfaces.
Cite
@article{arxiv.1906.08081,
title = {Derived equivalences of hyperk\"ahler varieties},
author = {Lenny Taelman},
journal= {arXiv preprint arXiv:1906.08081},
year = {2023}
}
Comments
(v5: reverted BBF form to standard normalisation; as was pointed out by Markman: the non-standard version did in general not take rational values )