The Yau-Tian-Donaldson Conjecture for general polarizations

TL;DR

This paper proves that for polarized algebraic manifolds, strong K-stability guarantees the existence of constant scalar curvature Kähler metrics, advancing the understanding of the Yau-Tian-Donaldson conjecture.

Contribution

It establishes the implication from strong K-stability to the existence of constant scalar curvature Kähler metrics for general polarizations.

Findings

Strong K-stability implies existence of cscK metrics.

Advances the Yau-Tian-Donaldson conjecture.

Provides new results for general polarizations.

Abstract

In this paper, assuming that a polarized algebraic manifold $(X,L)$ is strongly K-stable, we shall show that the polarization class $c_1(L)$ admits a constant scalar curvature Kaehler metric.