K-stability of constant scalar curvature K\"ahler manifolds

TL;DR

This paper proves that polarized manifolds with constant scalar curvature Kähler metrics and discrete automorphisms are K-stable, refining previous results that established only K-semistability, thus advancing the understanding of stability conditions in Kähler geometry.

Contribution

The paper establishes the K-stability of polarized manifolds with constant scalar curvature Kähler metrics and discrete automorphisms, strengthening prior K-semistability results.

Findings

Proves K-stability for manifolds with constant scalar curvature Kähler metrics.

Refines previous K-semistability results by Donaldson.

Enhances understanding of stability conditions in Kähler geometry.

Abstract

We show that a polarised manifold with a constant scalar curvature K\"ahler metric and discrete automorphisms is K-stable. This refines the K-semistability proved by S. K. Donaldson.