Futaki invariant and CM polarization

Gang Tian

doi:10.1007/978-4-431-56021-0_18

Futaki invariant and CM polarization

Gang Tian

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Scopus citations

Abstract

This is an expository paper. We will discuss various formulations of Futaki invariant and its relation to the CM line bundle. We will discuss their connections to the K-energy. We will also include proof for certain known results which may not have been well presented or less accessible in the literature. We always assume that M is a compact Kahler manifold. By a polarization, we mean a positive line bundle L over M, then we call (M, L) a polarized manifold.

Original language	English (US)
Title of host publication	Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014
Editors	Reiko Miyaoka, Akito Futaki, Weiping Zhang, Zizhou Tang
Publisher	Springer New York LLC
Pages	327-348
Number of pages	22
ISBN (Print)	9784431560197
DOIs	https://doi.org/10.1007/978-4-431-56021-0_18
State	Published - 2016
Event	10th Geometry Conference on Friendship between China and Japan, 2014 - Shanghai, China Duration: Sep 7 2014 → Sep 11 2014

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	154
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	10th Geometry Conference on Friendship between China and Japan, 2014
Country/Territory	China
City	Shanghai
Period	9/7/14 → 9/11/14

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

CM line bundle
CM-weight
Futaki invariant
Kähler-Einstein
Kählermetrics

Access to Document

10.1007/978-4-431-56021-0_18

Cite this

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title = "Futaki invariant and CM polarization",

abstract = "This is an expository paper. We will discuss various formulations of Futaki invariant and its relation to the CM line bundle. We will discuss their connections to the K-energy. We will also include proof for certain known results which may not have been well presented or less accessible in the literature. We always assume that M is a compact Kahler manifold. By a polarization, we mean a positive line bundle L over M, then we call (M, L) a polarized manifold.",

keywords = "CM line bundle, CM-weight, Futaki invariant, K{\"a}hler-Einstein, K{\"a}hlermetrics",

author = "Gang Tian",

note = "Publisher Copyright: {\textcopyright} Springer Japan 2016.; 10th Geometry Conference on Friendship between China and Japan, 2014 ; Conference date: 07-09-2014 Through 11-09-2014",

year = "2016",

doi = "10.1007/978-4-431-56021-0_18",

language = "English (US)",

isbn = "9784431560197",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "327--348",

editor = "Reiko Miyaoka and Akito Futaki and Weiping Zhang and Zizhou Tang",

booktitle = "Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014",

}

Tian, G 2016, Futaki invariant and CM polarization. in R Miyaoka, A Futaki, W Zhang & Z Tang (eds), Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014. Springer Proceedings in Mathematics and Statistics, vol. 154, Springer New York LLC, pp. 327-348, 10th Geometry Conference on Friendship between China and Japan, 2014, Shanghai, China, 9/7/14. https://doi.org/10.1007/978-4-431-56021-0_18

Futaki invariant and CM polarization. / Tian, Gang.
Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014. ed. / Reiko Miyaoka; Akito Futaki; Weiping Zhang; Zizhou Tang. Springer New York LLC, 2016. p. 327-348 (Springer Proceedings in Mathematics and Statistics; Vol. 154).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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T1 - Futaki invariant and CM polarization

AU - Tian, Gang

N1 - Publisher Copyright: © Springer Japan 2016.

PY - 2016

Y1 - 2016

N2 - This is an expository paper. We will discuss various formulations of Futaki invariant and its relation to the CM line bundle. We will discuss their connections to the K-energy. We will also include proof for certain known results which may not have been well presented or less accessible in the literature. We always assume that M is a compact Kahler manifold. By a polarization, we mean a positive line bundle L over M, then we call (M, L) a polarized manifold.

AB - This is an expository paper. We will discuss various formulations of Futaki invariant and its relation to the CM line bundle. We will discuss their connections to the K-energy. We will also include proof for certain known results which may not have been well presented or less accessible in the literature. We always assume that M is a compact Kahler manifold. By a polarization, we mean a positive line bundle L over M, then we call (M, L) a polarized manifold.

KW - CM line bundle

KW - CM-weight

KW - Futaki invariant

KW - Kähler-Einstein

KW - Kählermetrics

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U2 - 10.1007/978-4-431-56021-0_18

DO - 10.1007/978-4-431-56021-0_18

M3 - Conference contribution

AN - SCOPUS:84977489227

SN - 9784431560197

T3 - Springer Proceedings in Mathematics and Statistics

SP - 327

EP - 348

BT - Geometry and Topology of Manifolds - 10th China-Japan Geometry Conference, 2014

A2 - Miyaoka, Reiko

A2 - Futaki, Akito

A2 - Zhang, Weiping

A2 - Tang, Zizhou

PB - Springer New York LLC

T2 - 10th Geometry Conference on Friendship between China and Japan, 2014

Y2 - 7 September 2014 through 11 September 2014

ER -

Futaki invariant and CM polarization

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All Science Journal Classification (ASJC) codes

Keywords

Access to Document

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