Double EPW-sextics with actions of A7 and irrational GM threefolds

Published 2 Jul 2022 in math.AG | (2207.00833v3)

Abstract: We construct two examples of projective hyper-K\"ahler fourfolds of K3[2]-type with an action of the alternating group A7, making them some of the most symmetric hyper-K\"ahler fourfolds. They are realized as so called double EPW sextics and this allows us to construct an explicit family of irrational Gushel-Mukai threefolds.

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