Non-symplectic automorphisms of order 3 on K3 surfaces

TL;DR

This paper classifies non-symplectic automorphisms of order 3 on K3 surfaces, analyzing their fixed loci, cohomological actions, and the structure of the moduli space with three irreducible components.

Contribution

It provides a classification of fixed loci and describes the moduli space structure for K3 surfaces with such automorphisms, revealing three irreducible components.

Findings

Fixed locus topological structures are classified.

The automorphism action on cohomology is determined by fixed loci.

The moduli space has three irreducible components.

Abstract

In this paper we study K3 surfaces with a non-symplectic automorphism of order 3. In particular, we classify the topological structure of the fixed locus of such automorphisms and we show that it determines the action on cohomology. This allows us to describe the structure of the moduli space and to show that it has three irreducible components.