On Chow stability and balanced embeddings

TL;DR

This paper proves that Chow stability implies the existence of balanced embeddings for projective varieties, using the continuity method under certain technical conditions.

Contribution

It establishes a new implication from Chow stability to balanced embeddings, extending Zhang's result with a novel proof approach.

Findings

Chow stability implies the existence of balanced embeddings

The proof uses the continuity method under a technical hypothesis

Provides a new link between stability notions and embeddings

Abstract

An important result of Zhang states that for a projective variety, the existence of a balanced embedding is equivalent to Chow stability. In this paper, we shall prove that Chow stability implies that a balanced embedding exists via the continuity method. Our proof is conditional on a technical hypothesis about restrictions of Hamiltonians to subschemes of projective space.