Kahler-Einstein metrics on Fano manifolds, I: approximation of metrics with cone singularities

2012/11/19 by Xiuxiong Chen, Chen, Xiu-Xiong, Simon Donaldson +3 · 14 citations
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1211.4566

Abstract

This is the first of a series of three papers which provide proofs of results announced recently in arXiv:1210.7494.

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• Fully non-linear elliptic equations on noncompact complex manifolds
• An asymptotic slope of the α-K-energy for the Kahler-Yang-Mills equations
• Rigidity of complete Kähler-Einstein metrics under cscK perturbations
• Two Calabi-Yau theorems for degenerations of compact Kähler manifolds
• K-stability of Q-Fano Spherical Varieties via Compatible Divisors
• A transcendental non-Archimedean Calabi--Yau Theorem with applications to the cscK problem
• On the effective YTD conjecture
• Conical Kähler-Einstein metrics on K-unstable del Pezzo surfaces
• Hölder estimates for degenerate complex Monge-Ampère equations
• Alpha invariants and K-stability for general polarisations of Fano varieties
• K-stability of del Pezzo surfaces with a single quotient singularity
• Note on Poincaré type Kähler metrics and Futaki characters
• On the long time behaviour of the Conical Kähler- Ricci flows

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