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Analytic stability of the CR cross-cap. (English) Zbl 1123.32018
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.

##### MSC:
 32V40 Real submanifolds in complex manifolds 32S05 Local complex singularities
##### Keywords:
CR singularity; normal form; real submanifold
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