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Zbl 1123.32018
Coffman, Adam
Analytic stability of the CR cross-cap. (English)
[J] Pac. J. Math. 226, No. 2, 221-258 (2006). ISSN 0030-8730

The author shows that any real analytic submanifold of dimension $m$ of a complex space of dimension $n$ $(m< n)$ is locally equivalent via a holomorphic coordinate change to a fixed real algebraic variety defined by linear and quadratic polynomials. The situation is analogous to Whitney's stability theorem for cross-cap singularities of smooth maps. The complex analyticity of the normalizing transformation is proved using a rapid convergence argument.
[Viorel Vâjâitu (Bucureşti)]

MSC 2000:: *32V40 Real submanifolds in complex manifolds
32S05 Local singularities (analytic spaces)

Keywords: CR singularity; normal form; real submanifold

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