K-stability of constant scalar curvature polarization

TL;DR

This paper proves that polarized algebraic manifolds with a constant scalar curvature Kähler metric are K-stable, extending previous results and contributing to the understanding of stability conditions in complex geometry.

Contribution

It generalizes existing results by establishing K-stability for manifolds with constant scalar curvature polarization, based on new arguments and a forthcoming stronger stability concept.

Findings

K-stability holds for polarized algebraic manifolds with constant scalar curvature

Extends previous results by Chen-Tian, Donaldson, and Stoppa

Provides new methods based on a stronger concept of K-stability

Abstract

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." )