CM Stability And The Generalized Futaki Invariant II
Sean Timothy Paul, Gang Tian
Abstract
The Mabuchi K-energy map is exhibited as a singular metric on the refined CM polarization of any equivariant family Xp 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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