Theta-duality on Prym varieties and a Torelli Theorem

Details Theta-duality on Prym varieties and a Torelli Theorem Theta-duality on Prym varieties and a Torelli Theorem

2010-10-03

arxiv.org/abs/1010.0398v2

Mathematics

Algebraic Geometry

Final version to appear in Trans. Amer. Math. Soc

Scientific paper

Let p:C' -> C be an unramified double covering of irreducible smooth curves and let P be the attached Prym variety. We prove the schematic theta-dual equalities in the Prym variety T(C')=V^2 and T(V^2)=C', where V^2 is the Brill-Noether locus of P associated to p considered by Welters. As an application we prove a Torelli Theorem analogous to the fact that the g-th symmetric product of a curve D of genus g determines the curve.

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