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 : Ag generically injective if r > 6 and g > 2; r = 6 and g > 3; r = 4 and g > 5 or r = 2 and g > 6: We also show that a very general Prym variety of dimension at least 4 is not isogenous. The research that lead to the present paper was partially supported by a grant of the group GNSAGA of INdAM to a Jacobian.

Generic Torelli theorem for Prym varieties of ramified coverings

PIROLA, GIAN PIETRO
2012-01-01

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 : Rg;r : Ag generically injective if r > 6 and g > 2; r = 6 and g > 3; r = 4 and g > 5 or r = 2 and g > 6: We also show that a very general Prym variety of dimension at least 4 is not isogenous. The research that lead to the present paper was partially supported by a grant of the group GNSAGA of INdAM to a Jacobian.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/348928
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