Algebraic Geometry Seminar | Vanishing theorems for generalized pairs

Abstract 

A generalised pair is roughly a pair together with a nef divisor on a birational model. The theory of generalized pairs plays an important role in various aspects of birational geometry, such as the proof of the Borisov-Alexeev-Borisov conjecture. In this talk, I will discuss our recent works on the Kodaira vanishing theorem and the Kawamata-Viehweg vanishing theorem for lc generalized pairs. As an application, I will talk about a new proof of the base-point-freeness theorem for lc generalized pairs. This new approach allows us to prove the contraction theorem for lc generalized pairs without using Kollar's gluing theory. This is a joint work with Jihao Liu and Lingyao Xie.

About the speaker 

陈炳仪 Bingyi Chen

清华大学博士后，主要研究领域为双有理几何和奇点理论。具体研究的问题包括双有理几何中的有界性问题，以及奇点的不变量, 比如Hodge ideal等。曾获2017新世界数学学士论文金奖，ICCM2017最佳论文银奖，ICCM2022博士毕业论文金奖等。