Theta-duality on Prym varieties and a Torelli theorem

Lahoz, Martí; Naranjo, Juan Carlos

doi:10.1090/S0002-9947-2013-05675-9

Theta-duality on Prym varieties and a Torelli theorem
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by Martí Lahoz and Juan Carlos Naranjo PDF

Trans. Amer. Math. Soc. 365 (2013), 5051-5069 Request permission

Abstract:

Let $\pi : \widetilde C \to C$ be an unramified double covering of irreducible smooth curves and let $P$ be the attached Prym variety. We prove the scheme-theoretic theta-dual equalities in the Prym variety $T(\widetilde C)=V^2$ and $T(V^2)=\widetilde C$, where $V^2$ is the Brill-Noether locus of $P$ associated to $\pi$ considered by Welters. As an application we prove a Torelli theorem analogous to the fact that the symmetric product $D^{(g)}$ of a curve $D$ of genus $g$ determines the curve.

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