Angela Ortega, February 4, 2022

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 ├ętale 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.