Vector fields from locally invertible
polynomial maps in $\mathbb C^n$
Colloquium Mathematicum, Tome 140 (2015) no. 2, pp. 205-220
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $(F_1, \ldots , F_n): \mathbb {C}^n \to \mathbb {C}^{n}$ be a locally invertible polynomial map. We consider the canonical pull-back vector fields under this map, denoted by $\partial / \partial F_1, \ldots , \partial / \partial F_n $. Our main result is the following: if $n-1$ of the vector fields $\partial / \partial F_j$ have complete holomorphic flows along the typical fibers of the submersion $(F_1, \ldots , F_{j -1}, F_{j+1} , \ldots , F_n)$, then the inverse map exists. Several equivalent versions of this main hypothesis are given.
Keywords:
ldots mathbb mathbb locally invertible polynomial map consider canonical pull back vector fields under map denoted partial partial ldots partial partial main result following n vector fields partial partial have complete holomorphic flows along typical fibers submersion ldots ldots inverse map exists several equivalent versions main hypothesis given
Affiliations des auteurs :
Alvaro Bustinduy 1 ; Luis Giraldo 2 ; Jesús Muciño-Raymundo 3
@article{10_4064_cm140_2_4,
author = {Alvaro Bustinduy and Luis Giraldo and Jes\'us Muci\~no-Raymundo},
title = {Vector fields from locally invertible
polynomial maps in $\mathbb C^n$},
journal = {Colloquium Mathematicum},
pages = {205--220},
publisher = {mathdoc},
volume = {140},
number = {2},
year = {2015},
doi = {10.4064/cm140-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm140-2-4/}
}
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%0 Journal Article %A Alvaro Bustinduy %A Luis Giraldo %A Jesús Muciño-Raymundo %T Vector fields from locally invertible polynomial maps in $\mathbb C^n$ %J Colloquium Mathematicum %D 2015 %P 205-220 %V 140 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/cm140-2-4/ %R 10.4064/cm140-2-4 %G en %F 10_4064_cm140_2_4
Alvaro Bustinduy; Luis Giraldo; Jesús Muciño-Raymundo. Vector fields from locally invertible polynomial maps in $\mathbb C^n$. Colloquium Mathematicum, Tome 140 (2015) no. 2, pp. 205-220. doi: 10.4064/cm140-2-4
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