On CR singular CR images
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866911883844386816 |
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| author | Lebl, Jiří Noell, Alan Ravisankar, Sivaguru |
| author_facet | Lebl, Jiří Noell, Alan Ravisankar, Sivaguru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_01820 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On CR singular CR images Lebl, Jiří Noell, Alan Ravisankar, Sivaguru Complex Variables 32V05 (Primary), 32V30 (Secondary) 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. |
| title | On CR singular CR images |
| topic | Complex Variables 32V05 (Primary), 32V30 (Secondary) |
| url | https://arxiv.org/abs/2012.01820 |