%0 Journal Article %T K-stability of constant scalar curvature polarization %A Toshiki Mabuchi %J Mathematics %D 2008 %I arXiv %X In this paper, we shall show that a polarized algebraic manifold is K-stable if the polarization class admits a Kaehler metric of constant scalar curvature. This generalizes the results of Chen-Tian, Donaldson and Stoppa. (Parts of the arguments are based on a forthcoming paper "A stronger concept of K-stability." ) %U http://arxiv.org/abs/0812.4093v2