A CR singular analogue of Severi’s theorem
| Autor: | Jiri Lebl, Sivaguru Ravisankar, Alan Noell |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Quadric Mathematics - Complex Variables Mathematics::Complex Variables General Mathematics 010102 general mathematics Holomorphic function Order (ring theory) Codimension Extension (predicate logic) 01 natural sciences Flattening law.invention Invertible matrix Simple (abstract algebra) law 0103 physical sciences FOS: Mathematics Mathematics::Differential Geometry 010307 mathematical physics Complex Variables (math.CV) 0101 mathematics Mathematics::Symplectic Geometry 32V40 (Primary) 32V25 32V05 (Secondary) Mathematics |
| Zdroj: | Mathematische Zeitschrift. 299:1607-1629 |
| ISSN: | 1432-1823 0025-5874 |
| DOI: | 10.1007/s00209-021-02729-3 |
| Popis: | 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. Comment: 22 pages, accepted to Math. Z, fix hypothesis on Proposition 7.1 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink