The unirationality of $S_9^-$ and moduli spaces of pointed spin curves

Gavril Farkas; Alessandro Verra

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arXiv · 2604.18719

The unirationality of $S_9^-$ and moduli spaces of pointed spin curves

Gavril Farkas·Alessandro Verra

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Abstract

We show that the moduli space of odd spin curves of genus 9 is unirational. This is the highest genus for which such a result is known. This is achieved by realizing birationally the moduli space of odd spin curves of genus g<10 as a locally trivial projective bundle over a certain (finite quotient of the) moduli space of n-pointed odd stable spin curves of genus g'<g. We then present general results on the Kodaira dimension of both components of the moduli spaces of n-pointed spin curves of genus g.

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BibTeX RIS

Gavril Farkas, Alessandro Verra. 2026-04-20. The unirationality of $S_9^-$ and moduli spaces of pointed spin curves. https://arxiv.org/abs/2604.18719

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