Title: Minimal Model Program for Generalized Pairs
Speaker: Lingyao Xie
Speaker Info: University of Utah
Brief Description:
Special Note:
Abstract:
Generalized pairs were introduced by Birkar and Zhang in [BZ16] in their study of effective Iitaka fibrations, and later became a central topic in modern day birational geometry. For exmaple, the theory of generalized pairs is used to prove the Borisov-Alexeev-Borisov conjecture [Bir19,Bir21]. In this talk I will explain why we care about generalized pairs by showing that they naturally appear in the classification of algebraic varieties. Then I will discuss several recent fundamental results about generalized pairs. e.g Cone theorem ([Hacon-Liu21]), Contraction theorem ([Xie22]), Existence of flips ([Liu-Xie22]). If time permits, I will give the sketch of the proofs, and say something about Kollár's gluing theory, which is a key ingredient in our proofs. As an interesting corollary, we show that glc singularities are Du Bois.Date: Wednesday, February 01, 2023