Double EPW-sextics with actions of A7 and irrational GM threefolds
Simone Billi, Tomasz Wawak

TL;DR
This paper constructs highly symmetric hyper-K"ahler fourfolds with A7 actions as double EPW sextics and uses these to explicitly build a family of irrational Gushel-Mukai threefolds, advancing understanding of symmetries in complex geometry.
Contribution
It introduces new examples of symmetric hyper-K"ahler fourfolds with A7 actions and links them to irrational Gushel-Mukai threefolds through explicit constructions.
Findings
Construction of hyper-K"ahler fourfolds with A7 symmetry
Explicit family of irrational Gushel-Mukai threefolds
Identification of double EPW sextics as key geometric objects
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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Taxonomy
TopicsAdvanced Algebra and Geometry · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models
