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京东 11.11 红包
2023 AGSS Week 1 Lecture 4.1 Chenyang Xu
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Title: K-stability theory Speakers: Yuchen Liu (Northwestern), Xiaowei Wang (Rutgers), Chenyang Xu (Princeton), Jingjun Han (Fudan) Abstract: This course aims to overview the algebraic theory of K-stability for Fano varieties and discuss methods to describe K- moduli spaces for explicit Fano varieties. The topics include the valuative criterion of K-stability, construction of the K-moduli space and its properties, the wall crossing framework for K-moduli spaces of log Fano pairs, and their relations to GIT, moduli spaces of curves and K3 surfaces. Content: (1) The classical GIT stability and its relation to K-stability (2) Test configuration, numerical invariants, Fujita-Li’s valuative criterion (3) Boundedness of Fano varieties, openness of K-semistability, K-moduli stack (4) Good moduli space and properness of K-moduli space (5) Examples: K-moduli of log Fano pairs: surfaces and 3-folds
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