代数几何研讨班：How Are Generalized Pairs Applied in Foliation Theory?

数学研究所

学术报告

代数几何研讨班

报告人: 刘济豪 博士（北京大学）
    

题  目：How Are Generalized Pairs Applied in Foliation Theory?
   

时  间：2024.10.29（星期二）10：00-11：30
   

地  点：晨兴 410
   

摘  要：The concept of generalized pairs, introduced by Birkar and Zhang, plays an important

 role in modern birational geometry. This concept has been particularly crucial in proving the

 Borisov-Alexeev-Borisov conjecture and the McKernan-Shokurov conjecture. In this talk, 

I will explain how the theory of generalized pairs is applied to foliation theory from various 

perspectives, including but not limited to: Bertini-type theorems, the canonical bundle formula,

 the minimal model program (MMP) with scaling, the base-point-freeness theorem, the existence 

of flips, flops between minimal models, and the explicit adjunction formula. The talk is based on 

several joint works and ongoing collaborations with one or more of the following scholars: Paolo 

Cascini, Guodu Chen, Yifei Chen, Jingjun Han, Yujie Luo, Fanjun Meng, Calum Spicer, Roberto 

Svaldi, Yanze Wang, and Lingyao Xie.