CM STABILITY AND THE GENERALIZEDFUTAKI INVARIANT II

摘要

The Mabuchi K-energy map is exhibited as a singular metric on the refined CM polarization of any equivariant family X ~p→ 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.