Approximation and convergence of formal CR-mappings
| dc.creator | Meylan, Francine | |
| dc.creator | Mir, Nordine | |
| dc.creator | Zaitsev, Dmitri | |
| dc.date | 2002-05-14 | |
| dc.date.accessioned | 2026-07-07T04:48:29Z | |
| dc.date.available | 2026-07-07T04:48:29Z | |
| dc.description | Let $M\subset C^N$ be a minimal real-analytic CR-submanifold and $M'\subset C^{N'}$ a real-algebraic subset through points $p\in M$ and $p'\in M'$. We show that that any formal (holomorphic) mapping $f\colon (C^N,p)\to (C^{N'},p')$, sending $M$ into $M'$, can be approximated up to any given order at $p$ by a convergent map sending $M$ into $M'$. If $M$ is furthermore generic, we also show that any such map $f$, that is not convergent, must send (in an appropriate sense) $M$ into the set $E'\subset M'$ of points of D'Angelo infinite type. Therefore, if $M'$ does not contain any nontrivial complex-analytic subvariety through $p'$, any formal map $f$ as above is necessarily convergent. | |
| dc.identifier | https://arxiv.org/abs/math/0205151 | |
| dc.identifier | http://arxiv.org/abs/math/0205151 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64068 | |
| dc.subject | Complex Variables | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32H02, 32V20, 32V40 | |
| dc.title | Approximation and convergence of formal CR-mappings | |
| dc.type | text |