K3 surface entropy and automorphism groups

TL;DR

This paper characterizes complex projective K3 surfaces with automorphisms of positive entropy using their Néron-Severi lattices, classifies zero entropy cases with infinite automorphism groups, and identifies surfaces with almost abelian automorphism groups for Picard number ≥ 5.

Contribution

It provides a lattice-theoretic characterization of automorphism entropy and resolves longstanding questions about automorphism groups of K3 surfaces.

Findings

Characterization of K3 surfaces with positive entropy automorphisms

Classification of zero entropy K3 surfaces with infinite automorphism groups

Identification of K3 surfaces with almost abelian automorphism groups for Picard number ≥ 5

Abstract

We derive a characterization of the complex projective K3 surfaces which have automorphisms of positive entropy in term of their N\'eron-Severi lattices. Along the way, we classify the projective K3 surfaces of zero entropy with infinite automorphism groups and we determine the projective K3 surfaces of Picard number at least five with almost abelian automorphism groups, which gives an answer to a long standing question of Nikulin.