Generic Torelli theorem for Prym varieties of ramified coverings

Publisher： Cambridge University Press

E-ISSN： 1570-5846|148|4|1147-1170

ISSN： 0010-437x

Source： Compositio Mathematica, Vol.148, Iss.4, 2012-07, pp. : 1147-1170

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Abstract

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:ℛ g,r →𝒜 δ g−1+r/2 is generically injective if \[ rgt;6\text { and }g\geq 2,\quad r=6\text { and }g\geq 3,\quad r=4 \text { and }g\geq 5\quad \mbox {or}\quad r=2\text { and }g\geq 6. \] We also show that a very general Prym variety of dimension at least 4 is not isogenous to a Jacobian.

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