Cyclic groups of automorphisms of complex K3 surfaces

TL;DR

This paper classifies the possible orders of automorphisms of complex K3 surfaces, establishing a precise criterion based on Euler's totient function, which advances understanding of their symmetry properties.

Contribution

It provides a complete characterization of automorphism orders for complex K3 surfaces using a simple numerical condition involving Euler's totient function.

Findings

Automorphism order N satisfies φ(N) ≤ 20

Complete classification of automorphism orders for complex K3 surfaces

Establishment of a numerical criterion for automorphism orders

Abstract

We determine all possible orders of automorphisms of complex K3 surfaces. A positive integer N is the order of an automorphism of a complex K3 surface if and only if $\phi(N) \leq 20$ where $\phi$ is the Euler function.