2016/10/11 by Xianghong Gong, Gong, Xianghong, Laurent Stolovitch +1
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · doi:10.48550/arxiv.1610.03297
openalex publication_date 2016/10/11 · openalex created_date 2022/11/07 · openalex updated_date 2026/07/28
We study a germ of real analytic n-dimensional submanifold of Cn that has a complex tangent space of maximal dimension at a CR singularity. Under the condition that its complexification admits the maximum number of deck transformations, we first classify holomorphically its quadratic CR singularity. We then study its transformation to a normal form under the action of local (possibly formal) biholomorphisms at the singularity. We first conjugate formally its associated reversible map σ to suitable normal forms and show that all these normal forms can be divergent. We then construct a unique formal normal form under a non degeneracy condition.