| It has been recently proved that the existence of Kahler-Einstein metrics on compact complex manifold with {dollar}csb1(M) > 0{dollar} implies the K-stability and CM-stability of the underlying Kahler manifold (19). The criterion for the K-Stability is that the generalized Futaki invariant has non-negative real part on the central fiber. In the paper, we derive a formula computing the generalized Futaki invariant on the Q-Fano varieties with Brieskorn-Pham singularities and special isolated singularities(i.e. the tangent cone of the singular point is of hyperplanes). We also give some examples of K-stable manifolds. In particular, we show that K-stability on a cubic surface implies CM-stability. |
