Angela Ortega (Humboldt University, Berlin):
Generic Prym-Torelli theorem for ramified double coverings.
 
Abstract: Given a finite morphism between smooth curves one can canonically
associate it a polarised abelian variety, the Prym variety.  This induces a
map from the moduli space of coverings to the moduli space of polarised
abelian varieties, known as the Prym map.  It is a classical result that the
Prym map is generically injective for étale double coverings.

 In this talk we will give an introduction to the Prym varieties and maps. We
 will then consider the Prym map between the moduli space \mathcal{R}_{g,r} of
 double coverings over a genus g curve ramified at r points,
 \mathcal{A}^{\delta}_{g-1+r/2} the moduli space of polarized abelian
 varieties of dimension g-1+r/2 with polarisation of type \delta.  We will
 present a constructive proof of the generic injectivity of the Prym map when
 r \geq max{6, 2/3 (g+2)}.  This a joint work with J.C. Naranjo.