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An "Anti-Iitaka theorem" in positive characteristic

Event Category:
Valley Geometry Seminar
Iacopo Brivio
Center for Mathematical Sciences and Applications at Harvard University

Given a fibration $f\colon X\to Y$ of complex projective varieties with general fiber $F$, the Iitaka conjecture predicts the inequality $\kappa(K_X)\geq \kappa(K_F)+\kappa(K_Y)$. Recently Chang has shown that if one further assumes that the stable base locus $\mathbb{B}(-K_X)$ is vertical over $Y$, then we have a similar inequality 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 explain how to recover Chang's theorem for a large class of fibrations in positive characteristic.

Friday, May 10, 2024 - 4:00pm
LGRT 1681

Refreshments at 3:30pm