2014/09/26 by Ilya Kossovskiy, Kossovskiy, Ilya, Dmitri Zaitsev +1
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #math.CV
paper · pdf · doi:10.48550/arxiv.1409.7506
The paper in accepted to Advances in Mathematics. In this version, we revised the construction by normalizing the complex defining function of a real hypersurface instead of the real defining function. This is due to a remark of Martin Kolar who observed that using the real defining function leads to a singular ODE for a normalizing transformation in general
openalex publication_date 2014/09/26 · arxiv created 2015/06/07 · arxiv updated 2015/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the holomorphic equivalence problem for finite type hypersurfaces in \mathbb C2. We discover a geometric condition, which is sufficient for the existence of a natural convergent normal form for a finite type hypersurface. We also provide an explicit construction of such a normal form. As an application, we construct a canonical connection for a large class of finite type hypersurfaces. To the best of our knowledge, this gives the first construction of an invariant connection for Levi-degenerate hypersurfaces in \mathbb C2.