Iacopo Brivio (CMSA at Harvard)

Tuesday, January 23, 2024 - 1:45pm

PDL C-38

Title pre-talk: Some tools for positive characteristic fibrations

Abstract pre-talk: we first review the canonical bundle formula in characteristic zero and formulate an analogous result for F-split Calabi-Yau fibration. In the second part we'll recall the basics of foliation theory in positive characteristic and explain how they can be used to study "wild" fibrations.

Title: Anti Iitaka conjecture in positive characteristic

Abstract: Given a fibration of complex projective manifolds f:X---> Y with general fiber F, a famous conjecture due to Iitaka predicts the inequality \kappa(K_X)\geq \kappa(K_Y) +\kappa(K_F). If one assumes that the stable base locus of -K_X is vertical then a theorem of Chang establishes the inequality \kappa(-K_X)\leq \kappa(-K_Y) +\kappa(-K_F). Both Iitaka’s conjecture and Chang’s theorem are known to fail over fields of characteristic p>0. In this talk I am going to discuss a generalization of Chang’s result to fibrations in positive characteristic satisfying certain tameness conditions. This is based on a joint project with Marta Benozzo and Chi-Kang Chang.