Deformations of CR maps and applications

Abstract

We study the deformation theory of CR maps in the positive codimensional case. In particular, we study structural properties of the {\em mapping locus} $E$ of (germs of nondegenerate) holomorphic maps $H:(M,p)\to M^{\prime }$ between generic real submanifolds $M\subset {\mathbb{C}}^N$ and $M^{\prime }\subset {\mathbb{C}}^{N^{\prime }}$, defined to be the set of points $p^{\prime }\in M^{\prime }$ which admit such a map with $H(p)=p^{\prime }$. We show that this set $E$ is semi-analytic and provide examples for which $E$ posseses (prescribed) singularities.

References in corpus (1)

• Sufficient and necessary conditions for local rigidity of CR mappings and higher order infinitesimal deformations

Cited by in corpus (1)

• On highly degenerate CR maps of spheres