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.

33 pages, 8 figures

References in corpus (3)

• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• On the construction of Nadel multiplier ideal sheaves and the limiting behavior of the Ricci flow
• Kähler-Einstein metrics on smooth Fano symmetric varieties with Picard number one

Cited by in corpus (1)

• A Note On Kähler-Ricci Flow on Fano Threefolds