K-Stability of Fano spherical varieties

Abstract

We prove a criterion for K-stability of a $\mathbb{Q}$-Fano spherical variety with respect to equivariant special test configurations, in terms of its moment polytope and some combinatorial data associated to the open orbit. Combined with the equivariant version of the Yau-Tian-Donaldson conjecture for Fano manifolds proved by Datar and Székelyhidi, it yields a criterion for the existence of a Kähler-Einstein metric on a spherical Fano manifold. The results hold also for modified K-stability and existence of Kähler-Ricci solitons.

References in corpus (6)

• A variational approach to the Yau-Tian-Donaldson conjecture
• Sasaki-Einstein metrics and K-stability
• Kähler-Einstein metrics on group compactifications
• Toric degenerations of spherical varieties
• Kähler-Einstein metrics along the smooth continuity method
• Examples of K-unstable Fano manifolds with the Picard number one

Cited by in corpus (25)

• Kähler-Einstein metrics on group compactifications
• K-stability of Fano varieties: an algebro-geometric approach
• Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds
• Weighted K-stability and coercivity with applications to extremal Kahler and Sasaki metrics
• Uniform K-stability of polarized spherical varieties
• The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds
• Geometric quantization of coupled Kähler-Einstein metrics
• Kähler-Einstein metrics on smooth Fano symmetric varieties with Picard number one
• Singular limits of Kähler-Ricci flow on Fano $G$-manifolds
• Kähler-Ricci solitons on horospherical variety
• The moduli space of Fano manifolds with Kähler-Ricci solitons
• Examples of K-unstable Fano manifolds
• K-energy on polarized compactifications of Lie groups
• Fano manifolds and stability of tangent bundles
• K-stability of Gorenstein Fano group compactifications with rank two
• Volume minimization and obstructions to solving some problems in Kähler geometry
• Canonical blow-ups of Grassmann manifolds
• $G$-Sasaki manifolds and K-energy
• K-stable valuations and Calabi-Yau metrics on affine spherical varieties
• Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
• K-stability and polystable degenerations of polarized spherical varieties
• Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one
• Kähler-Einstein metrics and Ding functional on $\mathbb{Q}$-Fano group compactifications
• Kähler-Ricci flow on horospherical manifold
• Finiteness of $\mathbb{Q}$-Fano compactifications of semisimple group with Kähler-Einstein metrics