On the local algebraizability of real analytic generic submanifolds of C^n
| dc.creator | Gaussier, Herve | |
| dc.creator | Merker, Joel | |
| dc.date | 2004-03-16 | |
| dc.date.accessioned | 2026-07-07T05:06:28Z | |
| dc.date.available | 2026-07-07T05:06:28Z | |
| dc.description | We prove that the local (pseudo)group of biholomorphisms stabilizing a minimal, finitely nondegenerate real algebraic submanifold in C^n is a real algebraic local Lie group (the works of S.M. Baouendi, P. Ebenfelt, L.-P. Rothschild and D. Zaitsev published in this direction restrict, without understandable reason, to the isotropy group of a fixed central point). We deduce necessary conditions for the local algebraizability of real analytic rigid tubes of arbitrary codimension in C^n. Without using the Elie Cartan equivalence algorithm, we explain the up to now only known example Im w = e^(|z^2|), due to X. Huang, S. Ji and S.S. Yau in 2001, of a nonalgebraizable Levi nondegenerate real analytic hypersurface of C^2. These elementary criteria provide a first answer to an open problem raised by S.M. Baouendi, P. Ebenfelt and L.-P. Rothschild, in the survey article : ``Local geometric properties of real submanifolds in complex space'', Bull. Amer. Math. Soc. (N.S.) 37 (2000), no. 3, 309--336. A second answer (necessary and sufficient condition) for local algebraizability in the homogeneous case will appear subsequently. | |
| dc.description | Four pages, zero figures | |
| dc.identifier | https://arxiv.org/abs/math/0403275 | |
| dc.identifier | http://arxiv.org/abs/math/0403275 | |
| dc.identifier | C. R. Acad. Sci. Paris Ser. I 336 (2003) 125--128 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70483 | |
| dc.subject | Complex Variables | |
| dc.subject | Primary: 32V40. Secondary 32V25, 32H02, 32H40, 32V10 | |
| dc.title | On the local algebraizability of real analytic generic submanifolds of C^n | |
| dc.type | text |