Simple groups admit Beauville structures

We answer a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups other than the alternating group of degree 5 admit unmixed Beauville structures. We also consider an analog of the result for simple algebraic groups which depends on some upper bounds for character values of regular semisimple elements in finite groups of Lie type and obtain definitive results about the variety of triples in semisimple regular classes with product 1. Finally, we prove that any finite simple group contains two conjugacy classes C,D such that any pair of elements in C x D generates the group.Comment: 30 pages, in the second version, some results are improved and in particular we prove an irreducibility for a certain variet

New Beauville surfaces and finite simple groups

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

Beauville surfaces, moduli spaces and finite groups

In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with group either \PSL(2,p), or an alternating group, or a symmetric group or an abelian group. We moreover extend these results to regular surfaces isogenous to a higher product of curves.Comment: 27 pages. The article arXiv 0910.5402v2 was divided into two parts. This is the second half of the original paper, and it contains the subsections concerning the moduli spac

Series of pp-groups with Beauville structure

For every $p\geq 2$ we show that each finite $p$-group with an unmixed Beauville structure is part of a surjective infinite projective system of finite $p$-groups with compatible unmixed Beauville structures. This leads to the new notion of an unmixed topological Beauville structure on pro-finite groups. We further construct for $p \geq 5$ a new explicit infinite series of non-abelian $p$-groups that allow unmixed Beauville structures.Comment: 7 pages, to appear in: Monatshefte der Mathemati