Equivariant R-Test Configurations and Semistable Limits of Q-Fano Group Compactifications  

作　　者：Yan Li Zhenye Li 

机构地区：[1]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China [2]College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing 100029,China

出　　处：《Peking Mathematical Journal》2023年第2期559-607,共49页北京数学杂志（英文）

摘　　要：Let G be a connected,complex reductive group.In this paper,we classify G×G equivariant normal R-test configurations of a polarized G-compactification.Then,for Q-Fano G-compactifications,we express the H-invariants of their equivariant normal R-test configurations in terms of the combinatory data.Based onHan and Li“Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties”,we compute the semistable limit of aK-unstable FanoG-compactification.As an application,we show that for the two smooth K-unstable Fano SO4(C)-compactifications,the corresponding semistable limits are indeed the limit spaces of the normalized Kähler-Ricci flow.

关 键 词：Kähler-Ricci solitons Kähler-Ricci flow Q-Fano compactifications K-stability 

分 类 号：O17[理学—数学]