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

References in corpus (2)

• Degeneration of Kahler-Ricci solitons on Fano manifolds
• Regularity of Einstein Manifolds and the Codimension 4 Conjecture

Cited by in corpus (3)

• K stability and stability of chiral ring
• Orthogonal projection of a test configuration to vector fields
• Coupled Kähler-Einstein metrics