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arXiv · 2408.06962

Torsors of the Jacobians of the universal Fermat curves

Qixiao Ma
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Abstract

Let $m\geq3$ be an integer. We show that every torsor of the Jacobian of the universal family of degree-$m$ Fermat curve is necessarily a connected component of the Picard scheme. We show that the Jacobian of the generic degree-$m$ Fermat curve has uncountably many non-isomorphic torsors. We give some results towards the Franchetta type problem for torsors of the Jacobian of the universal family of genus-$g$ curves over $\mathcal{M}_g$.

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Qixiao Ma. 2024-08-13. Torsors of the Jacobians of the universal Fermat curves. https://arxiv.org/abs/2408.06962

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