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Vanishing thetanulls and hyperelliptic curves

Olivier Schneider
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Abstract

Let $\mathcal{M}_{g,2}$ be the moduli space of curves of genus $g$ with a level-2 structure. We prove here that there is always a non hyperelliptic element in the intersection of four thetanull divisors in $\mathcal{M}_{6,2}$. We prove also that for all $g\geqslant3$, each component of the hyperelliptic locus in $\mathcal{M}_{g,2}$ is a connected component of the intersection of $g-2$ thetanull divisors.

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Olivier Schneider. 2003-04-02. Vanishing thetanulls and hyperelliptic curves. https://arxiv.org/abs/math/0210196

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