Test configurations and Geodesic rays

2007/07/27 by Xiuxiong Chen, Chen, Xiuxiong, Yudong Tang +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0707.4149

openalex publication_date 2007/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For smooth test configurations, there always exist C^1,1 geodesic rays in Kahler metric space parallel to the algebraic ray. The \yen invariant agrees with Futaki invariant, at least under nice assumptions. Explicit examples in Toric cases are calculated. On simple test configurations, Donaldson's correspondence between HCMA solution and holomorphic disc family is extended.

Citations

• KÄHLER GEOMETRY OF TORIC VARIETIES AND EXTREMAL METRICS
• Geometry of Kähler Metrics and Foliations by Holomorphic Discs

Cited by

• Space of Kähler metrics (IV)--On the lower bound of the K-energy
• Note on geodesic rays tamed by simple test configurations

Related

• Test Configurations for K-Stability and Geodesic Rays
• Note on geodesic rays tamed by simple test configurations
• A remark on the Donaldson-Futaki invariant for sequences of test configurations
• On the regularity of geodesic rays associated to test configurations
• Analytic test configurations and geodesic rays