@article{df7095e153f14f329687769f3f71fc0b,
title = "G-uniform stability and K{\"a}hler–Einstein metrics on Fano varieties",
abstract = "Let X be any Q-Fano variety and Aut (X) be the identity component of the automorphism group of X. Let G be a connected reductive subgroup of Aut (X) that contains a maximal torus of Aut (X). We prove that X admits a K{\"a}hler–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.",
author = "Chi Li",
note = "Funding Information: The author is partially supported by NSF (Grant No. DMS-1810867) and an Alfred P. Sloan research fellowship. I would like to thank Gang Tian for constant support and his interest in this work, and thank Xiaowei Wang for helpful discussions on related topics, Feng Wang, Xiaohua Zhu and Chenyang Xu for helpful comments, S{\'e}bastien Boucksom for his interest in our work, and Tomoyuki Hisamoto for communications concerning Remark . I would like to thank Yuchen Liu for comments and clarifications, which motivate me to write down the results for more general reductive subgroups, and thank Jiyuan Han and Kuang-Ru Wu for attending my lectures about this work patiently and give valuable feedback which allows me to improve the presentation. I am particularly grateful to Jun Yu for answering my questions in the appendix concerning reductive groups. Some parts of this paper were written during the author{\textquoteright}s visit to BICMR at Peking University, School of Mathematical Sciences at Capital Normal University and Shanghai Center for Mathematical Sciences at Fudan University. I would like to thank these institutes for providing wonderful environment of research. In particular, I would like to thank Gang Tian, Zhenlei Zhang and Peng Wu for their hospitality. I would also like to thank anonymous referees for their careful reading and providing very helpful comments for improving the paper. Funding Information: The author is partially supported by NSF (Grant No. DMS-1810867) and an Alfred P. Sloan research fellowship. I would like to thank Gang Tian for constant support and his interest in this work, and thank Xiaowei Wang for helpful discussions on related topics, Feng Wang, Xiaohua Zhu and Chenyang Xu for helpful comments, S?bastien Boucksom for his interest in our work, and Tomoyuki Hisamoto for communications concerning Remark 5.10. I would like to thank Yuchen Liu for comments and clarifications, which motivate me to write down the results for more general reductive subgroups, and thank Jiyuan Han and Kuang-Ru Wu for attending my lectures about this work patiently and give valuable feedback which allows me to improve the presentation. I am particularly grateful to Jun Yu for answering my questions in the appendix concerning reductive groups. Some parts of this paper were written during the author?s visit to BICMR at Peking University, School of Mathematical Sciences at Capital Normal University and Shanghai Center for Mathematical Sciences at Fudan University. I would like to thank these institutes for providing wonderful environment of research. In particular, I would like to thank Gang Tian, Zhenlei Zhang and Peng Wu for their hospitality. I would also like to thank anonymous referees for their careful reading and providing very helpful comments for improving the paper. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2022",
month = feb,
doi = "10.1007/s00222-021-01075-9",
language = "English (US)",
volume = "227",
pages = "661--744",
journal = "Inventiones Mathematicae",
issn = "0020-9910",
publisher = "Springer New York",
number = "2",
}