Double EPW sextics associated to Gushel-Mukai surfaces
Algebraic Geometry
2025-01-03 v2
Abstract
Works by O'Grady allow to associate to a 2-dimensional Gushel-Mukai variety, which is a K3 surface, a double 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-K\"ahler manifolds. We also provide bounds for the automorphism group of Gushel-Mukai varieties in dimension 2 and higher.
Keywords
Cite
@article{arxiv.2011.12223,
title = {Double EPW sextics associated to Gushel-Mukai surfaces},
author = {Pietro Beri},
journal= {arXiv preprint arXiv:2011.12223},
year = {2025}
}
Comments
19 pages, results unchanged, many improvements in exposition. Title changed according to the referee. Final version