Surfaces isogenous to a product of curves, braid groups and mapping class groups

TL;DR

This paper explores the use of group theoretical methods to analyze the moduli space of surfaces of general type, specifically focusing on surfaces isogenous to a product of curves, and discusses bounds on their connected components.

Contribution

It introduces new group theoretical techniques to estimate the number of connected components in the moduli space of certain algebraic surfaces.

Findings

Bounds on the number of connected components derived

Application of braid groups and mapping class groups to surface classification

Enhanced understanding of surfaces isogenous to a product of curves

Abstract

This article is a revised version of the talk I gave at the conference ``Beauville Surfaces and groups'' held in Newcastle in June 2012. It presents some group theoretical methods to give bounds on the number of connected components of the moduli space of surfaces of general type, focusing on some families of regular surfaces isogenous to a product of curves.