The rationality of ineffective spin genus-4 thetanull loci

TL;DR

This paper proves that a certain divisor related to genus-4 curves with specific theta characteristics is a rational variety, extending the result to the Prym moduli space.

Contribution

It establishes the rationality of the divisor of genus-4 curves with a vanishing thetanull and ineffective thetacharacteristic, and extends this to the Prym moduli space.

Findings

The divisor of genus-4 curves with a vanishing thetanull is rational.

The analogous divisor in the Prym moduli space is also rational.

Provides a new geometric construction demonstrating rationality.

Abstract

In this paper, we show that the divisor given by couples [C,{\theta}] where C is a curve of genus 4 with a vanishing thetanull and {\theta} is an ineffective thetacharacteristic is a rational variety. By our construction, it follows also that the analogous divisor in the Prym moduli space is rational.