Kummer rigidity for K3 surface automorphisms via Ricci-flat metrics

TL;DR

This paper provides an alternative proof that automorphisms of K3 surfaces with maximal entropy measures are Kummer examples, utilizing Ricci-flat metrics and extending to non-projective cases.

Contribution

It introduces a new proof approach for Kummer rigidity on K3 surfaces using Ricci-flat metrics, broadening applicability to non-projective cases.

Findings

Automorphisms with maximal entropy are Kummer examples.

Ricci-flat metrics are instrumental in the proof.

The method applies to both projective and non-projective K3 surfaces.

Abstract

We give an alternative proof of a result of Cantat and Dupont, showing that any automorphism of a K3 surface with measure of maximal entropy in the Lebesgue class must be a Kummer example. Our method exploits the existence of Ricci-flat metrics on K3s and also covers the non-projective case.