On birational automorphisms of double EPW-cubes

TL;DR

This paper classifies finite symplectic birational automorphism groups on K3^[3]-type manifolds, describes automorphisms of double EPW-cubes, and provides examples of hyperkähler manifolds with large symmetry groups.

Contribution

It offers a detailed classification of symplectic automorphism groups on K3^[3]-type manifolds and describes automorphisms of double EPW-cubes, including explicit examples.

Findings

Classification of finite symplectic birational automorphism groups

Description of automorphism groups of double EPW-cubes

Examples of hyperkähler manifolds with maximal Picard rank and large symmetry groups

Abstract

We give a classification of finite groups of symplectic birational automorphisms on a manifold of K3^[3]-type with stable and stably saturated cohomological action. We describe the group of polarized automorphisms of a smooth double EPW-cube. Using this description, we exhibit examples of projective hyperkaehler manifolds of K3^[3]-type of maximal Picard rank with a symplectic action of a large group.