K3 surfaces with Picard number two

TL;DR

This paper investigates the automorphism groups of K3 surfaces with Picard number two, focusing on their generators and distinguishing between infinite cyclic and dihedral groups using spectral radius eigenvectors.

Contribution

It introduces a method to determine automorphism group generators and classifies the groups as cyclic or dihedral based on spectral analysis.

Findings

Automorphism groups are either infinite cyclic or dihedral.

Eigenvectors of spectral radius help identify generators.

Several examples illustrate the classification method.

Abstract

It is known that an automorphism group of a K3 surface with Picard number two is either infinite cyclic group or infinite dihedral group if it is infinite. In this paper, we study the generators of an automorphism group. We use the eigenvector corresponding to the spectral radius of an automorphism of infinite order to determine the generators. We also determine whether an automorphism group is the infinite cyclic group or the infinite dihedral group with several examples.