Related papers: K-stability and K\"ahler-Einstein metrics
We prove an existence result for twisted K\"ahler-Einstein metrics, assuming an appropriate twisted K-stability condition. An improvement over earlier results is that certain non-negative twisting forms are allowed.
We present classical and recent results on K\"ahler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI…
We make some observation on the logarithmic version of K-stability.
This paper extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
The second author has shown that existence of extremal K\"ahler metrics on semisimple principal toric fibrations is equivalent to a notion of weighted uniform K-stability, read off from the moment polytope. The purpose of this article is to…
We annnounce a proof of the fact that a K-stable Fano manifold admits a Kahler-Einstein metric and give a brief outline of the proof.
We study the existence of extremal K\"ahler metrics on K\"ahler manifolds. After introducing a notion of relative K-stability for K\"ahler manifolds, we prove that K\"ahler manifolds admitting extremal K\"ahler metrics are relatively…
We study logarithmic K-stability for pairs by extending the formula for Donaldson-Futaki invariants to log setting. We also provide algebro-geometric counterparts of recent results of existence of Kahler-Einstein metrics with cone…
We give an account of old and new results concerning many types of non-K\"ahler metrics, with focus on the problem of their coexistence on compact complex manifolds, and their behaviour at deformations and blow-up. We also describe a…
An introduction is provided to some current research trends in stability in geometric invariant theory and the problem of Kaehler metrics of constant scalar curvature. Besides classical notions such as Chow-Mumford stability, the emphasis…
For a holomorphic vector bundle over a compact K\"ahler orbifold, the slope stability of the bundle is shown to be equivalent to the existence of a Hermitian-Einstein metric or to the properness of a certain functional introduced by…
(One typo corrected and one incorrect statement removed. Extra details on conserved quantities and symmetry algebras added).
We survey some recent developments in the study of canonical K\"{a}hler metrics on algebraic varieties and their relation with stability in algebraic geometry.
This paper has been withdrawn in order to replace it by two separate submissions: 1. Hamiltonian 2-forms in Kahler geometry III: Extremal metrics and stability, math.DG/0511118; 2. Hamiltonian 2-forms in Kahler geometry IV: Weakly…
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 K\"ahler-Einstein metric. This is a strengthening of the solution of the…
We survey recent results on the existence of K\"ahler-Einstein metrics on certain smoothable Fano varieties, focusing on the importance of such metrics in the construction of compact algebraic moduli spaces of K-polystable Fano varieties.…
We extend an argument of Stoppa to make some prgress towards a proof that K\"ahler-Einstein manifolds are "b-stable". We point out some algebro-geometric questions, involving finite generation, that arise.
In this expository article we review the problem of finding Einstein metrics on compact K\"ahler manifolds and Sasaki manifolds. In the former half of this article we see that, in the K\"ahler case, the problem fits better with the notion…
We show that there exist K\"ahler-Einstein metrics on two exceptional Pasquier's two-orbits varieties. As an application, we will provide a new example of K-unstable Fano manifold with Picard number one.