时间：2024年8月9日/8月12日/8月13日/8月14日，14:00-16:00
地点：E4-201
主持人：Xin Fu, ITS
主讲人：Matsumura Shin- Ichi, Tohoku University
报告主题：A complex analytic aspect of the vanishing and injectivity theorems
报告摘要：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).
