On CR singular CR images

Abstract

We say that a CR singular submanifold [Formula: see text] has a removable CR singularity if the CR structure at the CR points of [Formula: see text] extends through the singularity as an abstract CR structure on [Formula: see text]. We study such real-analytic submanifolds, in which case removability is equivalent to [Formula: see text] being the image of a generic real-analytic submanifold [Formula: see text] under a holomorphic map that is a diffeomorphism of [Formula: see text] onto [Formula: see text], what we call a CR image. We study the stability of the CR singularity under perturbation, the associated quadratic invariants, and conditions for removability of a CR singularity. A lemma is also proved about perturbing away the zeros of holomorphic functions on CR submanifolds, which could be of independent interest.