Admissible metrics on compact Kähler varieties

2022/01/13 by Wenhao Ou, Ou, Wenhao
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2201.04821

openalex publication_date 2022/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a normal compact Kähler variety, and F a coherent reflexive sheaf on X. We investigate the existence of admissible Hermitian metrics on F. If moreover F is slope stable, we also study the existence of admissible Hermitian-Yang-Mills metrics on it. The existence will hold if one can prove a uniform Sobolev inequality on singular spaces.

Related

• Gauduchon metrics and Hermite-Einstein metrics on non-Kähler varieties
• Hermite--Einstein metrics in singular settings
• Hermitian-Yang-Mills connections on some complete non-compact Kähler manifolds
• Hermitian-Einstein metrics on stable vector bundles over compact Kähler orbifolds
• Admissible Hermitian-Yang-Mills connections over normal varieties