New Beauville surfaces and finite simple groups

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.Comment: v4: 18 pages. Final version, to appear in Manuscripta Mat