K-stability implies CM-stability

Gang Tian

Research output: Contribution to journalArticlepeer-review

3 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 languageEnglish (US)
Pages (from-to)245-261
Number of pages17
JournalProgress in Mathematics
Volume310
StatePublished - Jan 1 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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