# Symmetries of order eight on K3 surfaces without high genus curves in the fixed locus

## TL;DR

This paper classifies certain order-eight automorphisms on K3 surfaces, showing the fixed locus is either a rational curve plus isolated points or only isolated points, with explicit examples provided.

## Contribution

It provides a complete classification of non-symplectic automorphisms of order 8 on K3 surfaces under specific fixed locus conditions, including explicit examples.

## Key findings

- Fixed locus is either a rational curve plus 10 points or only 4 points.
- Explicit examples constructed for each fixed locus case.
- Classification advances understanding of symmetries on K3 surfaces.

## Abstract

In this paper we classify non-symplectic automorphisms of order 8 on complex K3 surfaces in case that the fourth power of the automorphism has only rational curves in its fixed locus. We show that the fixed locus is the disjoint union of a rational curve and 10 isolated points or it consists in 4 isolated fixed points. We give examples corresponding to the case with a rational curve in the fixed locus and to the case with only isolated points in the fixed locus.