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

• Autoři: KOSSOVSKIY Ilya; ZAITSEV Dmitri Mikhailowitch
• Rok publikování: 2019
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Journal für die Reine und Angewandte Mathematik
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• 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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• Klasifikační problémy pro reálné nadplochy v komplexním prostoru