Jefferson Baudin: An effective birational characterization of ordinary abelian varieties

Abstract:

Using generic vanishing theory, Chen and Hacon found a birational characterization of complex abelian varieties in any dimension by only fixing a few discrete invariants. More precisely, they showed that if a smooth projective complex variety \(X\) has first Betti number \(b_1(X) = 2\dim(X)\), and first two plurigenera \(h^0(X, \omega_X) = h^0(X, \omega_X^2) = 1\), then \(X\) is birational to an abelian variety.

Our goal is to present a positive characteristic analogue of this result, where we prove an effective birational characterization of ordinary abelian varieties, and establish additional statements.

We will explain how generic vanishing works (in both zero and positive characteristic), and how we can these techniques in our context.