Gauduchon metrics and Hermite-Einstein metrics on non-Kähler varieties

2025/03/04 by Pan, Chung-Ming · 1 citation
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.02759

Abstract

We show the existence of Gauduchon metrics on arbitrary compact hermitian varieties, generalizing our previous work on smoothable singularities. These metrics allow us to define the notion of slope stability for torsion-free coherent sheaves on compact normal varieties that are not necessarily Kähler. Then we prove the existence and uniqueness of singular Hermite-Einstein metrics for slope-stable reflexive sheaves on non-Kähler normal varieties.

Cited by

• Singular Gauduchon Conjecture

Related

• Hermite--Einstein metrics in singular settings
• Admissible metrics on compact Kähler varieties
• Hermitian-Einstein metrics on stable vector bundles over compact Kähler orbifolds
• Affine Hermitian-Einstein Metrics
• t-Gauduchon Ricci-flat metrics on non-Kähler Calabi-Yau manifolds