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

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10.1007/s11537-014-1387-3

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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",

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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

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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

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