CM Stability And The Generalized Futaki Invariant II

Details CM Stability And The Generalized Futaki Invariant II CM Stability And The Generalized Futaki Invariant II

2006-06-20

arxiv.org/abs/math/0606505v4

Mathematics

Differential Geometry

15, fully rewritten, references added

Scientific paper

The Mabuchi K-energy map is exhibited as a singular metric on the refined CM polarization of any equivariant family $\mathbf{X}\overset{p}{\to} S$. 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 $p$. Properness of the K-energy implies that the generalized Futaki invariant is strictly negative.

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