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.
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