Vol. 226, No. 2, 2006

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 274: 1
Vol. 273: 1  2
Vol. 272: 1  2
Vol. 271: 1  2
Vol. 270: 1  2
Vol. 269: 1  2
Vol. 268: 1  2
Vol. 267: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
Analytic stability of the CR cross-cap

Adam Coffman

Vol. 226 (2006), No. 2, 221–258
[an error occurred while processing this directive]

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