Characteristically simple beauville groups, II: Low rank and sporadic groups

Abstract

A Beauville surface is a rigid complex surface of general type, isogenous to a higher product by the free action of a finite group, called a Beauville group. Here we consider which characteristically simple groups can be Beauville groups. We show that if G is a cartesian power of a simple group L 2 (q), L 3 (q), U 3 (q), Sz(2 e), R(3 e), or of a sporadic simple group, then G is a Beauville group if and only if it has two generators and is not isomorphic to A 5.