2022/05/27 by Liviu Ornea, Misha Verbitsky, Ornea, Liviu +1
Mathematics · #14F06 #32L05 #32L10 #34C20 #53C07 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2205.14062
openalex publication_date 2022/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Mall bundle on a Hopf manifold H is a holomorphic vector bundle whose pullback to the universal cover of H is trivial. We define resonant and non-resonant Mall bundles, generalizing the notion of the resonance in ODE, and prove that a non-resonant Mall bundle always admits a flat holomorphic connection. We use this observation to prove a version of Poincare-Dulac linearization theorem, showing that any non-resonant invertible holomorphic contraction of a complex space is linear in appropriate holomorphic coordinates. We define the notion of resonance in Hopf manifolds, and show that all non-resonant Hopf manifolds are linear; previously, this result was obtained by Kodaira using the Poincare-Dulac theorem.