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Convergent normal form for real hypersurfaces at generic Levi degeneracy (1405.1743v1)
Published 7 May 2014 in math.CV and math.DG
Abstract: We construct a complete convergent normal form for a real hypersurface in $\CC{N},\,N\geq 2$ at generic Levi degeneracy. This seems to be the first convergent normal form for a Levi-degenerate hypersurface. In particular, we obtain, in the spirit of the work of Chern and Moser \cite{chern}, distinguished curves in the Levi degeneracy set, that we call \it degenerate chains.