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

  • Ilya Kossovskiy EMAIL logo and Dmitri Zaitsev
Published/Copyright: August 18, 2016

Abstract

We construct a complete convergent normal form for a real hypersurface in N, N2, 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 [6], distinguished curves inside the Levi-degeneracy set that we call degenerate chains.

Award Identifier / Grant number: 10/RFP/MTH2878

Funding statement: The first author was supported by the Austrian Science Foundation grant M1413-N25. The second author was supported in part by the Science Foundation Ireland grant 10/RFP/MTH2878.

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Received: 2015-07-06
Revised: 2016-02-11
Published Online: 2016-08-18
Published in Print: 2019-04-01

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