Beauville Surfaces, Moduli Spaces and Finite Groups

In this article 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. \ua9 2014 Copyright Taylor and Francis Group, LLC