Classification of non-symplectic automorphisms on K3 surfaces which act trivially on the N\'{e}ron-Severi lattice

TL;DR

This paper classifies non-symplectic automorphisms of prime-power order on K3 surfaces, focusing on those acting trivially on the Néron-Severi lattice, and describes their fixed loci.

Contribution

It provides a detailed classification of non-symplectic automorphisms of prime-power order on K3 surfaces, especially 2-power order, and characterizes their fixed points.

Findings

Classification of automorphisms of prime-power order

Description of fixed loci for these automorphisms

Focus on automorphisms acting trivially on Néron-Severi lattice

Abstract

We treat non-symplectic automorphisms on $K3$ surfaces which act trivially on the N\'{e}ron-Severi lattice. In this paper, we classify non-symplectic automorphisms of prime-power order, especially 2-power order on $K3$ surfaces, i.e., we describe their fixed locus.