The moduli space of odd spin curves of genus 9 is unirational, realized birationally as a locally trivial projective bundle over a finite quotient of the moduli space of n-pointed odd stable spin curves of lower genus.
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The unirationality of $S_9^-$ and moduli spaces of pointed spin curves
The moduli space of odd spin curves of genus 9 is unirational, realized birationally as a locally trivial projective bundle over a finite quotient of the moduli space of n-pointed odd stable spin curves of lower genus.