A moment map picture of relative balanced metrics on extremal Kähler manifolds

2017/03/28 by Yuji Sano, Sano, Yuji, Carl Tipler +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1703.09458

openalex publication_date 2017/03/28 · openalex created_date 2020/10/01 · openalex updated_date 2026/07/28

Abstract

We give a moment map interpretation of some relatively balanced metrics. As an application, we extend a result of S. K. Donaldson on constant scalar curvature Kähler metrics to the case of extremal metrics. Namely, we show that a given extremal metric is the limit of some specific relatively balanced metrics. As a corollary, we recover uniqueness and splitting results for extremal metrics in the polarized case.

Cited by

• Equivariant CM minimization for extremal manifolds

Related

• Stability of extremal Kähler manifolds
• Extremal Kähler metrics
• Extremal Kähler metrics on blowups
• Extremal metrics and lower bound of the modified K-energy
• Relative uniform K-stability over models implies existence of extremal metrics