Speaker
Description
Given a fibration of complex projective manifolds $f\colon X\to Y$ with general fiber $F$, the famous Iitaka conjecture predicts the inequality $\kappa(K_X)\geq \kappa(K_F)+\kappa(K_Y)$. Recently Chang has shown that, when the stable base locus of $-K_X$ is vertical over $Y$, a similar statement holds for the anticanonical divisor: $\kappa(-K_X)\leq \kappa(-K_F)+\kappa(-K_Y)$. Both Iitaka's conjecture and Chang's theorem are known to fail in positive characteristic. In this talk I will introduce a new class of "arithmetically general" positive characteristic varieties with negative canonical bundle, and show that Chang's theorem can be recovered when the general fiber $F$ belongs to this class. Based on joint work with Marta Benozzo and Chi-Kang Chang.
