K-stability of Gorenstein Fano group compactifications with rank two

Jae Hyouk Lee, Kyeong Dong Park, Sungmin Yoo

Research output: Contribution to journalArticlepeer-review


We give a classification of Gorenstein Fano bi-equivariant compactifications of semi-simple complex Lie groups with rank two, and determine which of them are equivariant K-stable and admit (singular) Kähler-Einstein metrics. As a consequence, we obtain several explicit examples of K-stable Fano varieties admitting (singular) Kähler-Einstein metrics. We also compute the greatest Ricci lower bounds, equivalently the delta invariants for K-unstable varieties. This gives us three new examples on which each solution of the Kähler-Ricci flow is of type II.

Original languageEnglish
Article number2250083
JournalInternational Journal of Mathematics
Issue number13
StatePublished - 1 Nov 2022

Bibliographical note

Publisher Copyright:
© 2022 World Scientific Publishing Company.


  • Gorenstein Fano group compactifications
  • Kähler-Ricci flow
  • Singular Kähler-Einstein metrics
  • equivariant K-stability
  • greatest Ricci lower bounds
  • moment polytopes


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