Convergent normal form for real hypersurfaces at a generic Levi-degeneracy
| Autoři | |
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| Rok publikování | 2019 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Journal für die Reine und Angewandte Mathematik |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | 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 |
| Klíčová slova | CR-geometry; holomorphic mappings; normal forms |
| Popis | 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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