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

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.