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CM Stability And The Generalized Futaki Invariant II

Differential Geometry 2008-04-23 v4 Algebraic Geometry

Abstract

The Mabuchi K-energy map is exhibited as a singular metric on the refined CM polarization of any equivariant family XpS\mathbf{X}\overset{p}{\to} S. Consequently we show that the generalized Futaki invariant is the leading term in the asymptotics of the reduced K-energy of the generic fiber of the map pp. Properness of the K-energy implies that the generalized Futaki invariant is strictly negative.

Cite

@article{arxiv.math/0606505,
  title  = {CM Stability And The Generalized Futaki Invariant II},
  author = {Sean Timothy Paul and Gang Tian},
  journal= {arXiv preprint arXiv:math/0606505},
  year   = {2008}
}

Comments

15, fully rewritten, references added

R2 v1 2026-07-22T17:37:43.628Z