Generic Torelli theorem for Prym varieties of ramified coverings

Abstract

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.

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

References in corpus (2)

• Hurwitz spaces of triple coverings of elliptic curves and moduli spaces of abelian threefolds
• The degree of the Gauss map for a general Prym Theta Divisor

Cited by in corpus (6)

• The fibers of the ramified Prym map
• On the Prym map for cyclic covers of genus two curves
• Involutions on hyperelliptic curves and Prym maps
• Geometry of Prym semicanonical pencils and an application to cubic threefolds
• Abelian covers and second fundamental form
• On the genus of curves in a Jacobian variety