Nelson Alvarado (Universidad de Chile) : Characterizations of polarized abelian varieties with a curve factor

In many aspects of the theory of algebraic curves (e.g Brill - Noether theory), the hyperelliptic ones are very special and they can be characterized in various ways. In this talk I will discuss one of those characterizations and show that it has a completely analogous conterpart in the context of polarized abelian varieties. Concretely, we show one characterization of the most special type of such varieties: products with at least one curve factor. This result deals with certain graded module over the ring of sections. If time allows it, I will discuss a second characterization of hyperelliptic curves, together with its abelian varieties analog, which deals with the non-surjectivity of certain Gauss-Wahl maps. This is a joint work with G. Pareschi.