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BIMSA AG Seminar
BIMSA AG Seminar
Subadditivity of anticanonical Iitaka dimension in characteristic p>0
Subadditivity of anticanonical Iitaka dimension in characteristic p>0
Organizers
Speaker
Iacopo Brivio
Time
Thursday, June 11, 2026 10:00 AM - 11:00 AM
Venue
A7-201
Online
Zoom 638 227 8222
(BIMSA)
Abstract
The Iitaka conjecture predicts that if $f:X \to Y$ is a fibration of smooth complex projective varieties and $y\in Y$ is a general point, then $\kappa(K_X)\geq \kappa(K_{X_y})+\kappa(K_Y)$. It was shown by Chang that, if the stable base locus $B(-K_X)$ does not dominate $Y$, then $\kappa(-K_X)\leq \kappa(-K_{X_y})+\kappa(-K_Y)$. Both the Iitaka conjecture and Chang's theorem are false in characteristic $p>0$. However the expectation is that one should be able to recover these inequalities when a general fiber is sufficiently "well behaved" with respect to the action of Frobenius. In this talk I will discuss how to recover Chang's theorem for such a class of fibrations, and discuss some related questions. This is based on a joint work with M. Benozzo and C.K. Chang.