A normal variety of invariant connections on hermitian symmetric spaces

2020/11/30 by Indranil Biswas, Biswas, Indranil, Harald Upmeier +1
Mathematics · #14M17 #32L05 #32M10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2011.15072

openalex publication_date 2020/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a class of G-invariant connections on a homogeneous principal bundle Q over a hermitian symmetric space M=G/K. The parameter space carries the structure of normal variety and has a canonical anti-holomorphic involution. The fixed points of the anti-holomorphic involution are precisely the integrable invariant complex structures on Q. This normal variety is closely related to quiver varieties and, more generally, to varieties of commuting matrix tuples modulo simultaneous conjugation.

Citations

• Homogeneous holomorphic hermitian principal bundles over hermitian symmetric spaces

Related

• Homogeneous holomorphic hermitian principal bundles over hermitian symmetric spaces
• Invariant operators on manifolds with almost Hermitian symmetric structures, II. Normal Cartan connections
• Admissible Hermitian-Yang-Mills connections over normal varieties
• Invariant Linear Connections on Homogeneous Symplectic Varieties
• Holomorphic normal projective connections on projective manifolds