Double EPW-cubes: automorphisms and degenerations

Simone Billi, Stevell Muller, Tomasz Wawak

Published 2024-05-24Version 1

We describe the group of naturally polarized automorphisms of a double EPW-cube. As an application, we exhibit examples of manifolds of K3^[3]-type with a symplectic action of a large group and determine their transcendental lattices. We study degenerations of smooth double EPW-cubes and give a resolution of mildly singular double EPW-cubes, this gives a family of hyperkaehler manifolds of K3^[3]-type whose general element is not birational to a moduli space of sheaves on a K3 surface.