Example of an order 16 non symplectic action on a K3 surface

TL;DR

This paper presents a specific example of a K3 surface with a non-symplectic automorphism of order 16, confirming a case in a known classification and advancing understanding of automorphism actions on K3 surfaces.

Contribution

It provides the first explicit example of a K3 surface with a non-symplectic automorphism of order 16, completing a classification case.

Findings

Constructed a K3 surface with Picard rank 14

Automorphism fixes a rational curve and 10 points

Completes the classification of non-symplectic automorphisms of order 16

Abstract

We exhibit an example of a K3 surface of Picard rank $14$ with a non-symplectic automorphism of order $16$ which fixes a rational curve and $10$ isolated points. This settles the existence problem for the last case of Al Tabbaa, Sarti and Taki's classification.