Non-symplectic automorphisms of order multiple of seven on K3 surfaces

TL;DR

This paper classifies non-symplectic automorphisms of K3 surfaces with orders multiple of seven, detailing their fixed loci and unifying results for various orders with new proofs and characterizations.

Contribution

It provides a comprehensive classification of non-symplectic automorphisms of orders multiple of seven on K3 surfaces, including new results for order 14 and unified proofs for orders 21, 28, and 42.

Findings

Complete characterization of fixed loci for these automorphisms.

New results for order 14 automorphisms.

Unified proofs for orders 21, 28, and 42.

Abstract

In this paper we present a classification of non-symplectic automorphisms of K3 surfaces whose order is a multiple of seven by describing the topological type of their fixed locus. In the case of purely non-symplectic automorphisms, we provide new results for order 14 and alternative proofs for orders 21, 28 and 42, so that we can unify in the same paper the results on these automorphisms. For each of these orders we also consider not purely non-symplectic automorphisms and obtain a complete characterization of their fixed loci. Several results of our paper were obtained independently in a recent paper by Brandhorst and Hofmann, but the methods used in the two papers are completely different.