On Ueno’s conjecture in positive characteristics

In characteristic zero, Ueno’s conjecture states that if X is a smooth projective variety with Kodaira dimension zero, then its Albanese morphism in an algebraic fiber space and the Kodaira dimension of the general fiber is again zero. This was proven by Cao and Păun in 2016.

Building on the generic vanishing techniques of Hacon and Patakfalvi, we prove a positive characteristic version of this result. We use it to deduce new cases of Iitaka’s subadditivity conjecture in positive characteristics. The goal of this talk is to explain how these techniques work, and how we can use them to prove such results.

For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar