K3 surface entropy and automorphism groups

Abstract

We derive a characterization of the complex projective K3 surfaces which have automorphisms of positive entropy in terms of their Néron–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.