On Automorphisms of Complex b^k-Manifolds

2023/10/12 by Tatyana Barron, Barron, Tatyana, Michael Francis +1
Mathematics · #32Q99 (Primary) 32M18 (Secondary) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2310.08014

openalex publication_date 2023/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The b-calculus of Melrose is a tool for studying structures on a smooth manifold with a first order degeneracy at a given hypersurface. In this framework, Mendoza defined complex b-manifolds. In the spirit of work of Scott, we extend Mendoza's definition to the case of higher-order degeneracies, introducing the notion of a complex b^k-manifold for k a positive integer. We then investigate the local and global automorphisms of complex b^k-manifolds. We also propose b^k-analogues for some classical spaces of holomorphic functions.

Related

• Automorphisms of \mathbb C^k and associated compact complex manifolds
• The Geometry of b^k Manifolds
• The Newlander-Nirenberg theorem for complex b-manifolds
• Characterization of the unit ball in \bf Cⁿ among complex manifolds of dimension n
• A note on the automorphism group of a compact complex manifold