Kähler-Einstein metrics along the smooth continuity method

Abstract

We show that if a Fano manifold $M$ is K-stable with respect to special degenerations equivariant under a compact group of automorphisms, then $M$ admits a Kähler-Einstein metric. This is a strengthening of the solution of the Yau-Tian-Donaldson conjecture for Fano manifolds by Chen-Donaldson-Sun, and can be used to obtain new examples of Kähler-Einstein manifolds. We also give analogous results for twisted Kähler-Einstein metrics and Kahler-Ricci solitons.

30 pages

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Cited by in corpus (9)

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• K-Stability of Fano spherical varieties
• Kähler-Einstein metrics on group compactifications
• Stability and coercivity for toric polarizations
• K stability and stability of chiral ring
• Torus equivariant K-stability
• Orthogonal projection of a test configuration to vector fields
• Singularity, Sasaki-Einstein manifold, Log del Pezzo surface and $\mathcal{N}=1$ AdS/CFT correspondence: Part I
• Coupled Kähler-Einstein metrics