Hermitian-Einstein metrics on stable vector bundles over compact Kähler orbifolds

2022/02/17 by Mitchell Faulk, Faulk, Mitchell · 3 citations
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2202.08885

Abstract

For a holomorphic vector bundle over a compact Kähler orbifold, the slope stability of the bundle is shown to be equivalent to the existence of a Hermitian-Einstein metric or to the properness of a certain functional introduced by Donaldson.

Cited by

• Orbifold Chern classes and Bogomolov-Gieseker inequalities
• On the Kobayashi-Hitchin correspondence for Kähler currents
• Orbifold Bogomolov-Gieseker inequalities on compact Kähler varieties

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• Existence of approximate Hermitian-Einstein structures on semi-stable bundles
• Affine Hermitian-Einstein Metrics
• Kobayashi-Hitchin correspondence for analytically stable bundles
• Hermitian-Yang-Mills connections on some complete non-compact Kähler manifolds
• Gauduchon metrics and Hermite-Einstein metrics on non-Kähler varieties