Dynamical degrees of automorphisms of K3 surfaces with Picard number 2

TL;DR

This paper investigates automorphisms of projective K3 surfaces with Picard number 2, identifying specific dynamical degrees and their properties, advancing understanding of their automorphism groups and dynamical behavior.

Contribution

It constructs an example of an automorphism with trace 3 on the Picard lattice and determines the set of possible dynamical degrees for such surfaces.

Findings

Existence of automorphism with trace 3 on Picard lattice

Complete characterization of dynamical degrees for Picard number 2

Extension of previous results by Hashimoto, Keum, and Lee

Abstract

We show that there exists an automorphism of a projective K3 surface with Picard number $2$ such that the trace of its action on the Picard lattice is $3$. Together with a result of K. Hashimoto, J. Keum and K. Lee, we determine the set of dynamical degrees of automorphisms of projective K3 surfaces with Picard number $2$.