Asymptotic polybalanced kernels on extremal Kaehler manifolds

TL;DR

This paper develops asymptotic polybalanced kernels on extremal Kähler manifolds, strengthening stability results and discussing stability notions related to the Yau-Tian-Donaldson conjecture.

Contribution

It introduces improved asymptotic polybalanced kernels and establishes stronger asymptotic stability results for extremal Kähler polarized manifolds.

Findings

Stronger asymptotic relative Chow-polystability established

Asymptotic polybalanced kernels constructed for extremal Kähler metrics

Discussion on differences between strong relative K-stability and relative K-stability

Abstract

In this paper, improving a preceding work, we obtain asymptotic polybalanced kernels associated to extremal Kaehler metrics on polarized algebraic manifolds. As a corollary, we have a stronger asymptotic relative Chow-polystability for extremal Kaehler polarized algebraic manifolds. Finally, related to the Yau-Tian-Donaldson Conjecture for extremal Kaehler metrics, we shall discuss the difference between strong relative K-stability and relative K-stability.