Beauville surfaces, moduli spaces and finite groups

TL;DR

This paper investigates the growth of the number of connected components in moduli spaces of surfaces of general type, focusing on Beauville surfaces with specific finite groups and extending results to higher product surfaces.

Contribution

It provides the asymptotic count of moduli space components for Beauville surfaces with various finite groups and extends the analysis to regular surfaces isogenous to a higher product.

Findings

Asymptotic growth rates for moduli space components are established.

Results cover groups like PSL(2,p), alternating, symmetric, and abelian groups.

Extensions to higher product surfaces are demonstrated.

Abstract

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.