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arXiv · 2607.17206

Torsors under the universal Jacobian over $\mathcal{M}_g$

Qixiao Ma
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Abstract

We consider the universal family of smooth genus-$g$ curves over $\mathbb{C}$. We show that for $g\geq4$, every torsor under the relative Jacobian is isomorphic to a connected component of the relative Picard scheme. As a byproduct, we show that $\mathrm{Br}(\mathcal{M}_{3,1})=\mathbb{Z}/2\mathbb{Z}$ over $\mathbb{C}$ and $\mathrm{H}_2(\Gamma_{3,1},\mathbb{Z})=\mathbb{Z}/2\mathbb{Z}$, pinning down the torsion subgroup in \cite[Theorem 1.2]{zbMATH01991000}.

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Qixiao Ma. 2026-07-19. Torsors under the universal Jacobian over $\mathcal{M}_g$. https://arxiv.org/abs/2607.17206

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