We will introduce the notion of K-stability by one parameter group degeneration. We will also introduce the generalized Futaki invariant and prove Theorem 1 of [LX14] (cf. Theorem 2.12 of [Xu]).

 

Ref.

[LX14] C. Li and C. Xu, Special test conguration and K-stability of Fano varieties, Ann. of Math. (2) 180 (2014), no. 1, 197-232.

[Xu] C. Xu, K-stability of Fano varieties: an algebro-geometric Approach