CMSA Member Seminar

Speaker: Iacopo Brivio (Harvard)

Title: Anti-Iitaka conjecture in positive characteristic

Abstract: Given a smooth projective variety, its Kodaira dimension kappa(K_X) is an important invariant that measures the rate of growth of m-pluricanonical forms as a function of m. It serves as an higher-dimensional generalization of the genus of a Riemann surface. If f : X –> Y is a fibration with general fiber F, a famous conjecture of Iitaka predicts the inequality kappa(K_X) \geq kappa(K_Y) + kappa(K_F). More recently it was shown by Chang that, if the stable base locus of -K_X is vertical, then the inequality kappa(-K_X) \leq kappa(-K_Y) + kappa(-K_F) holds. Both Iitaka’s conjecture and Chang’s theorem are known to fail in positive characteristic. In this talk I will explain how one can recover Chang’s theorem for a class of “tame” fibrations in characteristic p > 0. This is based on joint work with M. Benozzo and C.-K. Chang.