The moduli space of genus 4 even spin curves is rational

TL;DR

This paper proves that the moduli space of genus 4 even spin curves, characterized by a smooth genus 4 curve and a halfcanonical divisor with no global sections, is a rational variety using 3-fold Mori theory.

Contribution

It establishes the rationality of the moduli space of genus 4 even spin curves through advanced Mori theory techniques, providing new insights into its geometric structure.

Findings

The moduli space is rational.

The proof employs 3-fold Mori theory.

The result advances understanding of spin curve moduli spaces.

Abstract

By the technique of 3-fold Mori theory, we prove that the moduli space whose general point parameterizes a couple of a smooth curve of genus 4 and a halfcanonical divisor with vanishing global section is rational.