CM Stability And The Generalized Futaki Invariant II

摘要

The Mabuchi K-energy map is exhibited as a singular metric on the refined CMpolarization of any equivariant family $\mathbf{X}\overset{p}{\to} S$.Consequently we show that the generalized Futaki invariant is the leading termin 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 isstrictly negative.