Vol. 226, No. 2, 2006

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Analytic stability of the CR cross-cap

Adam Coffman

Vol. 226 (2006), No. 2, 221–258
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For m < n, any real analytic m-submanifold of complex n-space with a nondegenerate CR singularity is shown to be locally equivalent, under 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.

normal form, CR singularity, real submanifold
Mathematical Subject Classification 2000
Primary: 32V40, 32S05
Received: 5 December 2004
Accepted: 14 January 2006
Published: 1 August 2006
Adam Coffman
Department of Mathematical Sciences
Indiana Univ. - Purdue Univ. Fort Wayne
2101 E. Coliseum Blvd.
Fort Wayne, IN 46805-1499
United States