Giuseppe Pareschi: Two characterizations of decomposable principally polarized abelian varieties

Abstract:

A beautiful feature of curve theory is that curves with special geometry can be characterized by the failure of certain properties of suitable projective embeddings (normal generation, normal presentation, syzygies..). In turn this is equivalent to the failure of the surjectivity of certain uniformly defined linear maps.

Unfortunately in higher dimension there is almost nothing like that, not even for abelian varieties. Despite this, in this talk I will show that, among principally polarized abelian varieties, the decomposable ones, with a one-dimensional factor, are characterized by conditions similar to those of curve theory.