Analytic stability of the CR cross-cap

Adam Coffman

Vol. 226 (2006), No. 2, 221–258

DOI: 10.2140/pjm.2006.226.221

Abstract

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.

Keywords

normal form, CR singularity, real submanifold

Mathematical Subject Classification 2000

Primary: 32V40, 32S05

Milestones

Received: 5 December 2004

Accepted: 14 January 2006

Published: 1 August 2006