Year: 2023
Type: article
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 Q-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.
Source: Geometry & Topology
Author: Lenny Taelman
Institution: University of Amsterdam
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W2950829307