Automorphisms of surfaces: Kummer rigidity and measure of maximal entropy

TL;DR

This paper classifies complex projective surfaces with automorphisms of positive entropy that have a unique measure of maximal entropy absolutely continuous with respect to Lebesgue measure.

Contribution

It provides a classification of surfaces based on the properties of their automorphisms and invariant measures, focusing on Kummer rigidity.

Findings

Identifies conditions under which the measure of maximal entropy is absolutely continuous

Classifies surfaces with automorphisms of positive entropy exhibiting Kummer rigidity

Establishes a link between automorphism dynamics and measure-theoretic properties

Abstract

We classify complex projective surfaces with an automorphism of positive entropy for which the unique invariant measure of maximal entropy is absolutely continuous with respect to Lebesgue measure.