The rationality of ineffective spin genus-4 thetanull loci

Abstract

In this paper, we show that the divisor given by couples [C,θ] where C is a curve of genus 4 with a vanishing thetanull and θ 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.