The automorphism groups of certain singular K3 surfaces and an Enriques surface

TL;DR

This paper determines generators for the automorphism groups of three singular K3 surfaces with symplectic actions and an associated Enriques surface with Mathieu group action, advancing understanding of their symmetries.

Contribution

It provides explicit finite generators for the automorphism groups of specific singular K3 surfaces and an Enriques surface, linking their symmetries to well-known finite groups.

Findings

Generated automorphism groups for three singular K3 surfaces with symmetric group actions.

Identified generators for the automorphism group of an Enriques surface with Mathieu group action.

Connected surface symmetries to finite simple groups.

Abstract

We present finite sets of generators of the full automorphism groups of three singular K3 surfaces, on which the alternating group of degree 6 acts symplectically. We also present a finite set of generators of the full automorphism group of an associated Enriques surface, on which the Mathieu group M_{10} acts.