Free automorphisms of positive entropy on smooth K\"ahler surfaces

TL;DR

This paper demonstrates the existence of a projective K3 surface with a free automorphism of positive entropy and classifies smooth compact K"ahler surfaces admitting such automorphisms, showing only projective K3 surfaces and their blow-ups qualify.

Contribution

It proves the existence of a free automorphism of positive entropy on a projective K3 surface and classifies all smooth compact K"ahler surfaces with such automorphisms.

Findings

Existence of a projective K3 surface with a free automorphism of positive entropy

Only projective K3 surfaces and their blow-ups admit such automorphisms

Classification of smooth compact K"ahler surfaces with free automorphisms of positive entropy

Abstract

We prove that there is a projective K3 surface admitting a (fixed point) free automorphism of positive entropy and that no smooth compact K\"ahler surface other than projective K3 surfaces and their blow up admits such an automorphism.