Strong K-stability and asymptotic Chow-stability

TL;DR

This paper demonstrates that strong K-stability of a polarized algebraic manifold implies its asymptotic Chow-stability, establishing a link between these stability notions in algebraic geometry.

Contribution

It proves that strong relative K-stability implies asymptotic relative Chow-stability, clarifying the relationship between these stability concepts.

Findings

Strong relative K-stability implies asymptotic relative Chow-stability.

Asymptotic Chow-stability follows from strong K-stability when the torus is trivial.

The results connect different stability notions in the context of polarized algebraic manifolds.

Abstract

For a polarized algebraic manifold $(X,L)$, let $T$ be an algebraic torus in the group of all holomorphic automorphisms of $X$. Then strong relative K-stability will be shown to imply asymptotic relative Chow-stability. In particular, by taking $T$ to be trivial, we see that asymptotic Chow-stability follows from strong K-stability.