2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213720In 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." )Introduction of the version 1 is revisedDifferential GeometryAlgebraic Geometry53C55; 14L24text