Convergent normal form for real hypersurfaces at a generic Levi-degeneracy
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | Journal für die Reine und Angewandte Mathematik |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.degruyter.com/view/j/crelle.2019.2019.issue-749/crelle-2016-0034/crelle-2016-0034.xml |
| Doi | http://dx.doi.org/10.1515/crelle-2016-0034 |
| Keywords | CR-geometry; holomorphic mappings; normal forms |
| Description | We construct a complete convergent normal form for a real hypersurface in C^N for N>1 at a generic Levi-degeneracy. This seems to be the first convergent normal form for a Levi-degenerate hypersurface. As an application of the convergence result, we obtain an explicit description of the moduli space of germs of real-analytic hypersurfaces with a generic Levi-degeneracy. As another application, we obtain, in the spirit of the work of Chern and Moser, distinguished curves inside the Levi-degeneracy set that we call degenerate chains. |
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