Automorphisms of generalised Kummer fourfolds

TL;DR

This paper classifies automorphisms of generalised Kummer fourfolds, focusing on symplectic and non-symplectic automorphisms, using lattice theory and geometric analysis, and extends results to higher dimensions.

Contribution

It provides a comprehensive classification of automorphism groups of generalised Kummer fourfolds, including new results for finite symplectic automorphisms and partial classification for non-symplectic cases.

Findings

Classified non-symplectic prime order automorphisms.

Determined all finite order symplectic automorphism groups.

Extended results to higher-dimensional generalised Kummers.

Abstract

We classify non symplectic prime order automorphisms and all finite order symplectic automorphism groups of generalised Kummer fourfolds using lattice theory and recent results on ample cones and monodromy groups. We study various geometric realisations of the automorphisms obtained in the classification. In the case of higher dimensional generalised Kummers, we provide full results for finite symplectic automorphisms groups and we sketch the classification for prime order non-symplectic groups.