New Beauville surfaces and finite simple groups

TL;DR

This paper constructs new Beauville surfaces using finite simple groups, confirming a conjecture and leveraging probabilistic and classical group theory results.

Contribution

It introduces new Beauville surfaces associated with various finite simple groups, expanding the known examples and confirming a key conjecture.

Findings

Construction of Beauville surfaces with PSL(2,p^e) groups

Extension to other finite simple groups of Lie type

Verification of a conjecture by Bauer, Catanese, and Grunewald

Abstract

In this paper we construct new Beauville surfaces with group either $\PSL(2,p^e)$, or belonging to some other families of finite simple groups of Lie type of low Lie rank, or an alternating group, or a symmetric group, proving a conjecture of Bauer, Catanese and Grunewald. The proofs rely on probabilistic group theoretical results of Liebeck and Shalev, on classical results of Macbeath and on recent results of Marion.