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Theta-duality on Prym varieties and a Torelli theorem

Authors: Martí Lahoz and Juan Carlos Naranjo
Journal: Trans. Amer. Math. Soc. 365 (2013), 5051-5069
MSC (2010): Primary 14Kxx; Secondary 14Hxx
Published electronically: January 9, 2013
MathSciNet review: 3074366
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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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Additional Information

Martí Lahoz
Affiliation: Departament d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
Address at time of publication: Département de Mathématiques d’Orsay, Université Paris Sud 11, Bâtiment 425, F-91405 Orsay, France

Juan Carlos Naranjo
Affiliation: Departament d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain

Received by editor(s): December 1, 2010
Received by editor(s) in revised form: May 26, 2011, and July 25, 2011
Published electronically: January 9, 2013
Additional Notes: Both authors have been partially supported by the Proyecto de Investigación MTM2009-14163-C02-01. This paper was revised while the first-named author was supported by the SFB/TR 45 ‘Periods, Moduli Spaces and Arithmetic of Algebraic Varieties’ of the DFG (German Research Foundation)
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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