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arXiv · 2012.01820

On CR singular CR images

Jiří Lebl·Alan Noell·Sivaguru Ravisankar
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Abstract

We say that a CR singular submanifold $M$ has a removable CR singularity if the CR structure at the CR points of $M$ extends through the singularity as an abstract CR structure on $M$. We study such real-analytic submanifolds, in which case removability is equivalent to $M$ being the image of a generic real-analytic submanifold $N$ under a holomorphic map that is a diffeomorphism of $N$ onto $M$, 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.

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Jiří Lebl, Alan Noell, Sivaguru Ravisankar. 2020-12-03. On CR singular CR images. https://doi.org/10.1142/s0129167x21500907

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