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Generic Torelli theorem for Prym varieties of ramified coverings

Part of: Deformations of analytic structures Curves

Published online by Cambridge University Press:  11 July 2012

Valeria Ornella Marcucci  and
Gian Pietro Pirola
Valeria Ornella Marcucci
Affiliation:
Dipartimento di Matematica ‘F. Casorati’, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy (email: valeria.marcucci@unipv.it)
Gian Pietro Pirola
Affiliation:
Dipartimento di Matematica ‘F. Casorati’, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy (email: gianpietro.pirola@unipv.it)
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Abstract

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We consider the Prym map from the space of double coverings of a curve of genus g with r branch points to the moduli space of abelian varieties. We prove that 𝒫:ℛg,r→𝒜δg−1+r/2 is generically injective if We also show that a very general Prym variety of dimension at least 4 is not isogenous to a Jacobian.

Keywords

prym varietiesprym maptorelli theoremramified double coverings

MSC classification

Secondary: 14H40: Jacobians, Prym varieties 32G20: Period matrices, variation of Hodge structure; degenerations
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 4 , July 2012 , pp. 1147 - 1170
Copyright
Copyright © Foundation Compositio Mathematica 2012

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