Author:
Kossovskiy Ilya,Zaitsev Dmitri
Abstract
Abstract
We construct a complete convergent normal form for a real hypersurface in
{\mathbb{C}^{N}}
,
{N\geq 2}
, 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.
Funder
Science Foundation Ireland
Subject
Applied Mathematics,General Mathematics
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