Scalar curvature and projective embeddings, II

TL;DR

This paper demonstrates that on certain algebraic varieties, a constant scalar curvature Kähler metric uniquely minimizes the Mabuchi functional, using finite-dimensional approximation techniques.

Contribution

It introduces a new approach to prove the minimization of the Mabuchi functional by finite-dimensional approximation on polarized algebraic varieties.

Findings

Constant scalar curvature Kähler metric minimizes the Mabuchi functional.

Finite-dimensional approximation technique is effective in this context.

Results apply to polarized algebraic varieties without holomorphic vector fields.

Abstract

The paper uses the technique of finite-dimensional approximation to show that a constant scalr curvature Kahler metric (on a polarised algebraic variety without holomorphic vector fields) minimises the Mabuchi functional.