Harvard-MIT Algebraic Geometry Seminar: Superadditivity of anticanonical Iitaka dimension in positive characteristic
SEMINARS, HARVARD-MIT ALGEBRAIC GEOMETRY
Iacopo Brivio - CMSA
Given a fibration $f\colon X\to Y$ of smooth complex projective with general fiber $F$, the celebrated Iitaka conjecture predicts the inequality $\kappa(K_X)\geq \kappa(K_F)+\kappa(K_Y)$. Recently Chang showed that, under some natural conditions, the inequality $\kappa(-K_X)\leq \kappa(-K_F)+\kappa(-K_Y)$ holds.
In this talk I will show that, despite the failure in positive characteristic of both the Iitaka conjecture and Chang's theorem, it is possible to recover the latter for "tame" positive characteristic fibrations. This is based on joint work with M. Benozzo and C.-K. Chang.
For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar