About J-flow, J-balanced metrics, uniform J-stability and K-stability

2017/05/04 by Yoshinori Hashimoto, Hashimoto, Yoshinori, Julien Keller +1
Mathematics · Medicine · #14L24 #32Q15 #32Q25 #53C25 #53D50 #Alcohol Consumption and Health Effects #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1705.02000

openalex publication_date 2017/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

From the work of Dervan-Keller, there exists a quantization of the critical equation for the J-flow. This leads to the notion of J-balanced metrics. We prove that the existence of J-balanced metrics has a purely algebro-geometric characterization in terms of Chow stability, complementing the result of Dervan-Keller. We also obtain various criteria that imply uniform J-stability and uniform K-stability. Eventually, we discuss the case of Kähler classes that may not be integral over a compact manifold.

Citations

• A generalization of Ross-Thomas' slope theory
• Deformations from a given Kähler metric to a twisted cscK metric
• Uniform K-stability, Duistermaat-Heckman measures and singularities of\n pairs

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