The classification of purely non-symplectic automorphisms of high order on K3 surfaces

TL;DR

This paper classifies purely non-symplectic automorphisms of high order on K3 surfaces, focusing on cases where the Euler totient function of the order is at least 12, expanding understanding of their structure.

Contribution

It provides a comprehensive classification of purely non-symplectic automorphisms with high order on K3 surfaces for cases where (n)  12, a previously less understood area.

Findings

Complete classification for (n)  12

Identification of automorphism types with high order

Extension of known automorphism classifications

Abstract

An automorphism of order $n$ of a K3 surface is called purely non-symplectic if it multiplies the holomorphic symplectic form by a primitive $n$-th root of unity. We give the classification of purely non-symplectic automorphisms with $\varphi(n)\geq 12$ where $\varphi$ denotes the Euler totient function.