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Kodaira dimension and hyperbolicity for smooth families of varieties

Sung-Gi Park (Harvard)
Tuesday, November 15, 2022 - 1:45pm
PDL C-38
Pre-talk title: How many singular fibers are there?
Abstract: Given a family of varieties over a projective line, I will introduce various results around the minimum number of singular fibers.
Main talk title: 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.
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