Smooth covers of moduli stacks of Riemann surfaces with symmetry

TL;DR

This paper constructs an explicit finite cover of the moduli stack of compact Riemann surfaces with symmetries, resulting in a smooth quasi-projective variety, facilitating better geometric understanding.

Contribution

It provides the first explicit construction of smooth covers of moduli stacks of Riemann surfaces with symmetry groups.

Findings

Explicit finite cover constructed

Cover is smooth and quasi-projective

Enhances understanding of moduli stack geometry

Abstract

We construct explicitly a finite cover of the moduli stack of compact Riemann surfaces with a given group of symmetries by a smooth quasi-projective variety.