The fundamental group of quotients of a product of curves

TL;DR

This paper establishes a structure theorem for the fundamental group of quotients of products of curves by finite group actions, including resolutions of singularities, advancing understanding in algebraic geometry.

Contribution

It provides a new structural understanding of the fundamental groups of such quotients and their resolutions, which was previously not well-understood.

Findings

Structure theorem for fundamental groups of quotients

Applicable to resolutions of singularities

Enhances understanding of algebraic quotient spaces

Abstract

We prove a structure theorem for the fundamental group of the quotient $X$ of a product of curves by the action of a finite group $G$, hence for that of any resolution of the singularities of $X$.