G-uniform stability and Kahler-Einstein metrics on Fano varieties

• 成果类型: Article
• 署名作者: Li, Chi
• 署名单位: Purdue University System; Purdue University; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01075-9
• 发表日期: 2022
• 页码: 661-744
• 关键词: k-stability; energy; VALUATIONS; convexity; EXISTENCE; geometry; volumes; SPACES; bounds

摘要

Let X be any Q-Fano variety and Aut(X)(0) be the identity component of the automorphism group of X. Let G be a connected reductive subgroup of Aut(X)(0) that contains a maximal torus of Aut(X)(0). We prove that X admits a Kahler-Einstein metric if and only if X is G-uniformly K-stable. This proves a version of Yau-Tian-Donaldson conjecture for arbitrary singular Fano varieties. A key new ingredient is a valuative criterion for G-uniform K-stability.