A stronger concept of K-stability

TL;DR

This paper introduces a broader class of test configurations to strengthen the definition of K-stability, facilitating progress in proving that constant scalar curvature metrics imply K-stability for polarized algebraic manifolds.

Contribution

It proposes a new, more inclusive concept of K-stability using extended one-parameter group actions, advancing the understanding of the stability condition.

Findings

Established a stronger form of K-stability

Enabled key steps in proving the link between scalar curvature and K-stability

Provided a framework for future research in algebraic geometry

Abstract

In this paper, by introducing a wider class of one-parameter group actions for test configurations, we have a stronger form of the definition of K-stability. This allows us to obtain some key step of my preceding work in proving that constant scalar curvature polarization implies K-stability for polarized algebraic manifolds.