Related papers: Kahler-Einstein metrics and algebraic geometry
This is an expository article, closely following the author's lecture at the 2014 Journal Differential Geometry conference.
This is a survey article, based on the author's lectures in the 2015 AMS Summer Research Institute in Algebraic Geometry, and to appear in the Proceedings.
In recent years, there are many progress made in K\"ahler geometry. In particular, the topics related to the problems of the existence and uniqueness of extremal K\"ahler metrics, as well as obstructions to the existence of such metrics in…
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 discuss how metric limits and rescalings of K\"ahler-Einstein metrics connect with Algebraic Geometry, mostly in relation to the study of moduli spaces of varieties, and singularities. Along the way, we describe some elementary examples,…
We survey selected developments in the metric geometry of the space of K\"ahler metrics, emphasizing results from the past decade, highlighting open problems along the way.
This is a survey article, to appear in the Proceedings of the 2018 International Congress of Mathematicians. (Revised, with added and updated references.)
In this new version, we correct some typos. For the readers' convenience, we also added some footnotes and more details for certain lemmas and theorems.
Smooth Kahler-Einstein metrics have been studied for the past 80 years. More recently, singular Kahler-Einstein metrics have emerged as objects of intrinsic interest, both in differential and algebraic geometry, as well as a powerful tool…
This is a survey of recent contributions to the area of special Kaehler geometry. It is based on lectures given at the 21st Winter School on Geometry and Physics held in Srni in January 2001.
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 extends our earlier results to higher dimensions using a different approach, based on the rigidity of complex structures on certain domains.
We survey some recent results and constructions of almost-K\"ahler manifolds whose curvature tensors have certain algebraic symmetries. This is an updated and corrected version of the (to be) published manuscript.
Chapters 1 to 4 are the lecture notes of my course "Real Algebraic Geometry I" from the winter term 2020/2021. Chapters 5 to 8 are the lecture notes of its continuation "Real Algebraic Geometry II" from the summer term 2021. Chapters 9 and…
This is a sequel to the survey given by the author in Surveys in Differential Geometry Vol. 6 in 1999. The present survey covers selected developments since 1999 to 2011 dealing with the construction of Einstein metrics on bundles and…
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…
This is a survey article of the recent progresses on the metric behaviour of Ricci-flat K\"{a}hler-Einstein metrics along degenerations of Calabi-Yau manifolds.
This is a double exposure of the probabilistic construction of Kahler-Einstein metrics on a complex projective algebraic variety X - where the Kahler-Einstein metric emerges from a canonical random point process on X - and the variational…
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…
In this work we study the intrinsic geometry of the space of Kahler metrics under various Riemannian metrics. The first part is on the Dirichlet metric. We motivate its study, we compute its curvature, and we make links with the Calabi…