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Stability conditions and
moduli spaces for Kuznetsov components of Gushel–Mukai
varieties
Alexander Perry, Laura Pertusi and Xiaolei Zhao |
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Geometry & Topology 26 (2022) 3055–3121
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Abstract |
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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
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Mathematical Subject Classification
Primary: 14F08, 14J28, 14J45
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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
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Authors |
| Alexander Perry | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
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| http://www-personal.umich.edu/~arper/ | |
| Laura Pertusi | |
| Dipartimento di Matematica Federigo
Enriques Università degli Studi di Milano Milano Italy |
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| http://www.mat.unimi.it/users/pertusi/index.html | |
| Xiaolei Zhao | |
| Department of Mathematics University of California, Santa Barbara Santa Barbara, CA United States |
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| https://sites.google.com/site/xiaoleizhaoswebsite/ | |
