The fundamental group and torsion group of Beauville surfaces

Abstract

We give a survey on the fundamental group of surfaces isogenous to a higher product. If the surfaces are regular, e.g. if they are Beauville surfaces, the first homology group is a finite group. We present a MAGMA script which calculates the first homology groups of regular surfaces isogenous to a product.

14 pages; MAGMA script included; v2: minor corrections, final version to appear in the Proceedings of the Conference "Beauville Surfaces and Groups", Newcastle University (UK), 7-9th June 2012