A note on the definition of K-stability

2011/11/24 by Jacopo Stoppa, Stoppa, Jacopo · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.1111.5826

2 pages

arxiv created 2011/11/24 · openalex publication_date 2011/11/24 · arxiv updated 2011/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As recently pointed out by Li and Xu, the definition of K-stability, and the author's proof of K-stability for cscK manifolds without holomorphic vector fields, need to be altered slightly: the Donaldson-Futaki invariant is positive for all test configurations which are not trivial in codimension 2.

Citations

• Special test configurations and K-stability of Fano varieties
• Filtrations and test-configurations

Cited by

• Uniform K-stability, Duistermaat-Heckman measures and singularities of\n pairs

Related

• Filtrations and test-configurations
• A stronger concept of K-stability
• The Donaldson-Futaki invariant for sequences of test configurations
• K-stability implies CM-stability
• K-stability for Kähler Manifolds