Westlake Math Colloquium第三十九期 | Lingyao Xie: Minimal model program for generalized pairs

2023-06-13 10:29:51



主持人:理论科学研究院 陈国度博士

主讲人: 犹他大学 谢灵尧博士

讲座主题Minimal model program for generalized pairs


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 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 the Minimal Model Program of generalized log canonical pairs, e.g. Cone theorem ([Hancon-Liu21]), Contraction theorem ([Xie22]), Existence of flips ([Liu-Xie22]), some terminations ([Tsa-Xie23]). The key ingredient in our proofs is Koll\'ar's gluing theory. As some interesting corollaries, we show that glc singularities are Du Bois and the Kodaira vanishing theorem for generalized pairs ([CLX23]).