Kodaira dimension and hyperbolicity for smooth families of varieties

Abstract: In this talk, I will discuss the behavior of positivity, hyperbolicity, and Kodaira dimension under smooth morphisms of complex quasi-projective manifolds. This includes a vast generalization of a classical result: a fibration from a projective surface of non-negative Kodaira dimension to a projective line has at least three singular fibers. Furthermore, I will explain a proof of Popa's conjecture on the superadditivity of the log Kodaira dimension over bases of dimension at most three. These theorems are applications of the main technical result, namely the logarithmic base change theorem.

algebraic geometry

Audience: researchers in the topic

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com