Publication details

Convergent normal form for real hypersurfaces at a generic Levi-degeneracy

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KOSSOVSKIY Ilya ZAITSEV Dmitri Mikhailowitch

Year of publication 2019
Type Article in Periodical
Magazine / Source Journal für die Reine und Angewandte Mathematik
MU Faculty or unit

Faculty of Science

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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