A CR singular analogue of Severi's theorem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866910455410196480 |
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| author | Lebl, Jiri Noell, Alan Ravisankar, Sivaguru |
| author_facet | Lebl, Jiri Noell, Alan Ravisankar, Sivaguru |
| contents | Real-analytic CR functions on real-analytic CR singular submanifolds are not in general restrictions of holomorphic functions, unlike in the CR nonsingular case. We give a simple condition that completely characterizes those quadric CR singular manifolds of codimension 2 in ${\mathbb C}^{n+1}$ for which an extension result holds. Consequently, we obtain an extension result for general real-analytic CR singular submanifolds of codimension 2. As applications we give a condition for the flattening of such submanifolds, and we classify CR singular images of CR submanifolds up to second order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_04752 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A CR singular analogue of Severi's theorem Lebl, Jiri Noell, Alan Ravisankar, Sivaguru Complex Variables 32V40 (Primary) 32V25, 32V05 (Secondary) Real-analytic CR functions on real-analytic CR singular submanifolds are not in general restrictions of holomorphic functions, unlike in the CR nonsingular case. We give a simple condition that completely characterizes those quadric CR singular manifolds of codimension 2 in ${\mathbb C}^{n+1}$ for which an extension result holds. Consequently, we obtain an extension result for general real-analytic CR singular submanifolds of codimension 2. As applications we give a condition for the flattening of such submanifolds, and we classify CR singular images of CR submanifolds up to second order. |
| title | A CR singular analogue of Severi's theorem |
| topic | Complex Variables 32V40 (Primary) 32V25, 32V05 (Secondary) |
| url | https://arxiv.org/abs/1909.04752 |