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arXiv · 2502.07197

A note on multisecants of the Kummer variety of a Jacobian

Robert Auffarth·Sebastián Rahausen
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Abstract

We show that if $C$ is a smooth projective curve and $\mathfrak{d}$ is a $\mathfrak{g}^{n}_{2n}$ on $C$, then we obtain a rational map $\mathrm{Sym}^{n}(C)\dashrightarrow\mathfrak{d}$ whose fibers can be related in an interesting way to Gunning multisecants of the Kummer variety of $JC$. This generalizes previous work done by the first author with Codogni and Salvati Manni.

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Robert Auffarth, Sebastián Rahausen. 2025-02-11. A note on multisecants of the Kummer variety of a Jacobian. https://arxiv.org/abs/2502.07197

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