Kähler–Einstein metrics on Fano manifolds

Gang Tian

doi:10.1007/s11537-014-1387-3

Kähler–Einstein metrics on Fano manifolds

Gang Tian

Mathematics

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

6 Scopus citations

Abstract

This is an expository paper on Kähler metrics of positive scalar curvature. It is for my Takagi Lectures at RIMS in November of 2013. In this paper, I first discuss the Futaki invariants, the K-stability and its relation to the K-energy. Next I will outline my work in 2012 on the existence of Kähler–Einstein metrics on K-stable Fano manifolds. Finally, I will present S. Paul’s work on stability of pairs with some modifications of mine.

Original language	English (US)
Pages (from-to)	1-41
Number of pages	41
Journal	Japanese Journal of Mathematics
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/s11537-014-1387-3
State	Published - Mar 2015

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Futaki invariant
K-stability
Kähler–Einstein
manifold
metrics
partial C-estimate

Access to Document

10.1007/s11537-014-1387-3

Cite this

@article{095a9ab8373e423e8e67e386ef4d0e52,

title = "K{\"a}hler–Einstein metrics on Fano manifolds",

abstract = "This is an expository paper on K{\"a}hler metrics of positive scalar curvature. It is for my Takagi Lectures at RIMS in November of 2013. In this paper, I first discuss the Futaki invariants, the K-stability and its relation to the K-energy. Next I will outline my work in 2012 on the existence of K{\"a}hler–Einstein metrics on K-stable Fano manifolds. Finally, I will present S. Paul{\textquoteright}s work on stability of pairs with some modifications of mine.",

keywords = "Futaki invariant, K-stability, K{\"a}hler–Einstein, manifold, metrics, partial C-estimate",

author = "Gang Tian",

note = "Publisher Copyright: {\textcopyright} 2014, The Mathematical Society of Japan and Springer Japan.",

year = "2015",

month = mar,

doi = "10.1007/s11537-014-1387-3",

language = "English (US)",

volume = "10",

pages = "1--41",

journal = "Japanese Journal of Mathematics",

issn = "0289-2316",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - Kähler–Einstein metrics on Fano manifolds

AU - Tian, Gang

PY - 2015/3

Y1 - 2015/3

N2 - This is an expository paper on Kähler metrics of positive scalar curvature. It is for my Takagi Lectures at RIMS in November of 2013. In this paper, I first discuss the Futaki invariants, the K-stability and its relation to the K-energy. Next I will outline my work in 2012 on the existence of Kähler–Einstein metrics on K-stable Fano manifolds. Finally, I will present S. Paul’s work on stability of pairs with some modifications of mine.

AB - This is an expository paper on Kähler metrics of positive scalar curvature. It is for my Takagi Lectures at RIMS in November of 2013. In this paper, I first discuss the Futaki invariants, the K-stability and its relation to the K-energy. Next I will outline my work in 2012 on the existence of Kähler–Einstein metrics on K-stable Fano manifolds. Finally, I will present S. Paul’s work on stability of pairs with some modifications of mine.

KW - Futaki invariant

KW - K-stability

KW - Kähler–Einstein

KW - manifold

KW - metrics

KW - partial C-estimate

UR - https://www.scopus.com/pages/publications/84925491643

UR - https://www.scopus.com/pages/publications/84925491643#tab=citedBy

U2 - 10.1007/s11537-014-1387-3

DO - 10.1007/s11537-014-1387-3

M3 - Article

AN - SCOPUS:84925491643

SN - 0289-2316

VL - 10

SP - 1

EP - 41

JO - Japanese Journal of Mathematics

JF - Japanese Journal of Mathematics

IS - 1

ER -

Kähler–Einstein metrics on Fano manifolds

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this