Nonalgebraizable real analytic tubes in C^n
| dc.creator | Gaussier, Hervé | |
| dc.creator | Merker, Joël | |
| dc.date | 2004-04-13 | |
| dc.date.accessioned | 2026-07-07T05:07:25Z | |
| dc.date.available | 2026-07-07T05:07:25Z | |
| dc.description | We give necessary conditions for certain real analytic tube generic submanifolds in C^n to be locally algebraizable. As an application, we exhibit families of real analytic non locally algebraizable tube generic submanifolds in C^n. During the proof, we show that the local CR automorphism group of a minimal, finitely nondegenerate real algebraic generic submanifold is a real algebraic local Lie group. We may state one of the main results as follows. Let M be a real analytic hypersurface tube in C^n passing through the origin, having a defining equation of the form v = ϕ(y), where (z,w)= (x+iy,u+iv) \in C^{n-1} \times C. Assume that M is Levi nondegenerate at the origin and that the real Lie algebra of local infinitesimal CR automorphisms of M is of minimal possible dimension n, i.e. generated by the real parts of the holomorphic vector fields \partial_{z_1}, ..., \partial_{z_{n-1}}, \partial_w. Then M is locally algebraizable only if every second derivative \partial^2_{y_ky_l}ϕis an algebraic function of the collection of first derivatives \partial_{y_1} ϕ,..., \partial_{y_m} ϕ. | |
| dc.description | 36 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0404250 | |
| dc.identifier | http://arxiv.org/abs/math/0404250 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70853 | |
| dc.subject | Complex Variables | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Differential Geometry | |
| dc.subject | Primary: 32V40. Secondary 32V25, 32H02, 32H40, 32V10 | |
| dc.title | Nonalgebraizable real analytic tubes in C^n | |
| dc.type | text |