A note on multisecants of the Kummer variety of a Jacobian

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 \(\textrm{Sym}^{n}(C)\dashrightarrow \mathfrak {d}\) 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.