K-stability of Gorenstein Fano group compactifications with rank two
Abstract
We give a classification of Gorenstein Fano bi-equivariant compactifications of semisimple 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2022
- DOI:
- 10.48550/arXiv.2203.11058
- arXiv:
- arXiv:2203.11058
- Bibcode:
- 2022arXiv220311058L
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Algebraic Geometry;
- Mathematics - Complex Variables;
- Primary: 14M27;
- 32Q20;
- Secondary: 32M12;
- 53C55
- E-Print:
- 33 pages, 8 figures