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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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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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
  • Email: marti.lahoz@ub.edu
  • Juan Carlos Naranjo
  • Affiliation: Departament d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
  • MR Author ID: 318430
  • ORCID: 0000-0003-1989-4924
  • Email: jcnaranjo@ub.edu
  • 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)
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 5051-5069
  • MSC (2010): Primary 14Kxx; Secondary 14Hxx
  • DOI: https://doi.org/10.1090/S0002-9947-2013-05675-9
  • MathSciNet review: 3074366