Generic Torelli theorem for Prym varieties of ramified coverings

Details Generic Torelli theorem for Prym varieties of ramified coverings Generic Torelli theorem for Prym varieties of ramified coverings

2010-10-21

arxiv.org/abs/1010.4483v3

Mathematics

Algebraic Geometry

24 pages, 2 figures. One reference added. To appear in Compositio Mathematica

Scientific paper

In this paper we prove that 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, is generically injective if r>6 and g>1, r=6 and g>2, r=4 and g>4,
r=2 and g>5. We also show that a very generic Prym variety of dimension at
least 4 is not isogenous to a Jacobian.

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