The moduli space of \'etale double covers of genus 5 curves is unirational

TL;DR

This paper proves that the moduli space of étale double covers of genus 5 curves is unirational, using geometric and computational methods, advancing understanding of the structure of these moduli spaces.

Contribution

The paper establishes the unirationality of the moduli space of étale double covers of genus 5 curves, providing two distinct proofs—geometric and computational.

Findings

The moduli space R_5 is shown to be unirational.

Two different proofs of the main result are provided.

The results contribute to the classification of moduli spaces of algebraic curves.

Abstract

We show that the coarse moduli space $\cR_5$ of \'etale double covers of curves of genus~5 over the complex numbers is unirational. We give two slightly different arguments, one purely geometric and the other more computational.