A note on multisecants of the Kummer variety of a Jacobian

We show that if $C$ is a smooth projective curve and $\mathfrak{d}$ is a ${\mathfrak{g}}_{2n}^n$ on $C$, then we obtain a rational map ${\mathrm{S}\mathrm{y}\mathrm{m}}^n(C)⇢\mathfrak{d}$ 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.