On CR singular CR images
| Autor: | Alan Noell, Sivaguru Ravisankar, Jiř 'ı Lebl |
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| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Mathematics - Complex Variables Mathematics::Complex Variables General Mathematics Astrophysics::Instrumentation and Methods for Astrophysics Structure (category theory) Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Submanifold Singularity FOS: Mathematics 32V05 (Primary) 32V30 (Secondary) Computer Science::General Literature Complex Variables (math.CV) Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | International Journal of Mathematics. 32 |
| ISSN: | 1793-6519 0129-167X |
| DOI: | 10.1142/s0129167x21500907 |
| Popis: | 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. Comment: 22 pages, accepted to Internat. J. Math |
| Databáze: | OpenAIRE |
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