Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches 2π and completion of the main proof

Xiu Xiong Chen; Simon Donaldson; Song Sun

doi:10.1090/S0894-0347-2014-00801-8

Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches 2π and completion of the main proof

Xiu Xiong Chen
, Simon Donaldson
, Song Sun

Mathematics

Imperial College London

Research output: Contribution to journal › Article › peer-review

236 Scopus citations

Abstract

This is the third and final article in a series which prove the fact that a K-stable Fano manifold admits a Kähler-Einstein metric.In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle approaches 2π We also put all our technical results together to complete the proof of the main theorem.

Original language	English
Pages (from-to)	235-278
Number of pages	44
Journal	Journal of the American Mathematical Society
Volume	28
Issue number	1
DOIs	https://doi.org/10.1090/S0894-0347-2014-00801-8
State	Published - Jan 1 2015

Access to Document

10.1090/S0894-0347-2014-00801-8

Cite this

@article{9ec574b33287425aa8cde2386f5307e8,

title = "K{\"a}hler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches 2π and completion of the main proof",

abstract = "This is the third and final article in a series which prove the fact that a K-stable Fano manifold admits a K{\"a}hler-Einstein metric.In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle approaches 2π We also put all our technical results together to complete the proof of the main theorem.",

author = "Chen, \{Xiu Xiong\} and Simon Donaldson and Song Sun",

note = "Publisher Copyright: {\textcopyright} 2014, American Mathematical Society.",

year = "2015",

month = jan,

day = "1",

doi = "10.1090/S0894-0347-2014-00801-8",

language = "English",

volume = "28",

pages = "235--278",

journal = "Journal of the American Mathematical Society",

issn = "0894-0347",

number = "1",

}

TY - JOUR

T1 - Kähler-Einstein metrics on Fano manifolds. III

T2 - Limits as cone angle approaches 2π and completion of the main proof

AU - Chen, Xiu Xiong

AU - Donaldson, Simon

AU - Sun, Song

PY - 2015/1/1

Y1 - 2015/1/1

N2 - This is the third and final article in a series which prove the fact that a K-stable Fano manifold admits a Kähler-Einstein metric.In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle approaches 2π We also put all our technical results together to complete the proof of the main theorem.

AB - This is the third and final article in a series which prove the fact that a K-stable Fano manifold admits a Kähler-Einstein metric.In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle approaches 2π We also put all our technical results together to complete the proof of the main theorem.

UR - https://www.scopus.com/pages/publications/84924754698

U2 - 10.1090/S0894-0347-2014-00801-8

DO - 10.1090/S0894-0347-2014-00801-8

M3 - Article

AN - SCOPUS:84924754698

SN - 0894-0347

VL - 28

SP - 235

EP - 278

JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

IS - 1

ER -

Kähler-Einstein metrics on Fano manifolds. III: Limits as cone angle approaches 2π and completion of the main proof

Abstract

Access to Document

Other files and links

Fingerprint

Cite this