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Stability conditions and moduli spaces for Kuznetsov components of Gushel–Mukai varieties

Alexander Perry, Laura Pertusi and Xiaolei Zhao

Geometry & Topology 26 (2022) 3055–3121
Abstract

We prove the existence of Bridgeland stability conditions on the Kuznetsov components of Gushel–Mukai varieties, and describe the structure of moduli spaces of Bridgeland semistable objects in these categories in the even-dimensional case. As applications, we construct a new infinite series of unirational locally complete families of polarized hyperkähler varieties of K3 type, and characterize Hodge-theoretically when the Kuznetsov component of an even-dimensional Gushel–Mukai variety is equivalent to the derived category of a K3 surface.

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Keywords
stability conditions, Gushel–Mukai varieties, semiorthogonal decompositions, K3 surfaces, hyperkähler manifolds
Mathematical Subject Classification
Primary: 14F08, 14J28, 14J45
References
Publication
Received: 28 July 2020
Revised: 2 July 2021
Accepted: 17 August 2021
Published: 23 January 2023
Proposed: Richard P Thomas
Seconded: Paul Seidel, Dan Abramovich
Authors
Alexander Perry
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States
http://www-personal.umich.edu/~arper/
Laura Pertusi
Dipartimento di Matematica Federigo Enriques
Università degli Studi di Milano
Milano
Italy
http://www.mat.unimi.it/users/pertusi/index.html
Xiaolei Zhao
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA
United States
https://sites.google.com/site/xiaoleizhaoswebsite/