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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:
32V40Real submanifolds in complex manifolds
32S05Local singularities (analytic spaces)