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arXiv · 2203.11058

K-stability of Gorenstein Fano group compactifications with rank two

Jae-Hyouk Lee·Kyeong-Dong Park·Sungmin Yoo
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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) K\"{a}hler-Einstein metrics. As a consequence, we obtain several explicit examples of K-stable Fano varieties admitting (singular) K\"{a}hler-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 K\"{a}hler-Ricci flow is of type II.

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Jae-Hyouk Lee, Kyeong-Dong Park, Sungmin Yoo. 2022-03-21. K-stability of Gorenstein Fano group compactifications with rank two. https://doi.org/10.1142/s0129167x22500835

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