Time：14:00-16:00, August 9/12/13/14, 2024
Venue：E4-201
Host：Xin Fu, ITS
Speaker：Matsumura Shin- Ichi, Tohoku University
Title: A complex analytic aspect of the vanishing and injectivity theorems
Abstract：In this intensive course, I will discuss generalizations of the vanishing theorem using complex geometric and analytic methods. The goal of this course is to explain my recent results on the complex analytic theory of the injectivity theorem for varieties with log canonical (LC) singularities.
Here the injectivity theorem is a generalization of Kodaira's vanishing theorem to line bundles with "semi-positive" curvature.
First, I will start with the basic notions of complex geometry (such as vector bundles, Hermitian metrics, and Chern curvature) and I will introduce Kollar's injectivity theorem, which is a generalization to "semi-positive" line bundles, and Enoki's injectivity theorem, its complex geometric analogue. Next, I will introduce singular Hermitian metrics and multiplier ideals and prove their generalization to KLT singularities. Finally, I will introduce a generalization to LC singularities and provide an outline of the proof.
A part of this talk is joint work with Tsz On Mario Chan and Young-Jun Choi (Pusan National University).
