Title: Generically finite Prym maps

Abstract: Given a finite morphism between smooth projective curves one can canonically associate it a polarized abelian variety, the Prym variety. This induces a map from the moduli space of coverings to the moduli space of polarized abelian varieties, known as the Prym map.

Unlike the classical case of étale double coverings over curves of genus at least 7, when the Prym map is generically injective (and never injective), we prove in a joint work with J.C. Naranjo, the global injectivity of the Prym map for ramified double coverings over curves of genus g ≥ 1 and ramified in at least 6 points.

I will finish the talk with a brief overview on what is known on the degree of generically finite Prym maps.