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Double EPW sextics associated with Gushel–Mukai surfaces

Part of: Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  23 December 2024

Pietro Beri
Pietro Beri*
Affiliation:
Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75013 Paris, France (beri@imj-prg.fr)
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Abstract

Works by O’Grady allow to associate with a two-dimensional Gushel–Mukai (GM) variety, which is a K3 surface, a double Eisenbud–Popescu–Walter (EPW) sextic. We characterize the $K3$ surfaces whose associated double EPW sextic is smooth. As a consequence, we are able to produce symplectic actions on some families of smooth double EPW sextics which are hyper-Kähler manifolds.

We also provide bounds for the automorphism group of GM varieties in dimension 2 and higher.

Keywords

K3 surfaceshyper-Kähler manifoldsautomorphismsFano varieties

MSC classification

Primary: 14J28: $K3$ surfaces and Enriques surfaces
Secondary: 14J35: $4$-folds 14J50: Automorphisms of surfaces and higher-dimensional varieties 14J10: Families, moduli, classification
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 22
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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