K-stability implies CM-stability

Gang Tian

doi:10.1007/978-3-319-49638-2_11

K-stability implies CM-stability

Gang Tian

Mathematics

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

8 Scopus citations

Abstract

In this paper, we prove in details that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper. Our proof is based on an asymptotic formula for the K-energy and S. Paul’s works ([Pa08], [Pa12], [Pa13]) on the K-stability in terms of stable pairs.

Original language	English (US)
Pages (from-to)	245-261
Number of pages	17
Journal	Progress in Mathematics
Volume	310
DOIs	https://doi.org/10.1007/978-3-319-49638-2_11
State	Published - 2017

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology

Keywords

CM-weight
Determinant line bundle
K-stability
Polarization

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10.1007/978-3-319-49638-2_11

Cite this

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title = "K-stability implies CM-stability",

abstract = "In this paper, we prove in details that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper. Our proof is based on an asymptotic formula for the K-energy and S. Paul{\textquoteright}s works ([Pa08], [Pa12], [Pa13]) on the K-stability in terms of stable pairs.",

keywords = "CM-weight, Determinant line bundle, K-stability, Polarization",

author = "Gang Tian",

note = "Publisher Copyright: {\textcopyright} 2017 Springer International Publishing.",

year = "2017",

doi = "10.1007/978-3-319-49638-2_11",

language = "English (US)",

volume = "310",

pages = "245--261",

journal = "Progress in Mathematics",

issn = "0743-1643",

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TY - JOUR

T1 - K-stability implies CM-stability

AU - Tian, Gang

PY - 2017

Y1 - 2017

N2 - In this paper, we prove in details that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper. Our proof is based on an asymptotic formula for the K-energy and S. Paul’s works ([Pa08], [Pa12], [Pa13]) on the K-stability in terms of stable pairs.

AB - In this paper, we prove in details that any polarized K-stable manifold is CM-stable. This extends what I did for Fano manifolds in my 2012 paper. Our proof is based on an asymptotic formula for the K-energy and S. Paul’s works ([Pa08], [Pa12], [Pa13]) on the K-stability in terms of stable pairs.

KW - CM-weight

KW - Determinant line bundle

KW - K-stability

KW - Polarization

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UR - http://www.scopus.com/inward/citedby.url?scp=85019125771&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-49638-2_11

DO - 10.1007/978-3-319-49638-2_11

M3 - Article

AN - SCOPUS:85019125771

SN - 0743-1643

VL - 310

SP - 245

EP - 261

JO - Progress in Mathematics

JF - Progress in Mathematics

ER -

K-stability implies CM-stability

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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