Vector fields from locally invertible polynomial maps in ℂⁿ

Alvaro Bustinduy, Luis Giraldo, and Jesús Muciño-Raymundo. "Vector fields from locally invertible polynomial maps in ℂⁿ." Colloquium Mathematicae 140.2 (2015): 205-220. <http://eudml.org/doc/283735>.

@article{AlvaroBustinduy2015,
abstract = {Let (F₁,..., Fₙ): ℂⁿ → ℂⁿ be a locally invertible polynomial map. We consider the canonical pull-back vector fields under this map, denoted by ∂/∂F₁,...,∂/∂Fₙ. Our main result is the following: if n-1 of the vector fields $∂/∂F_\{j\}$ have complete holomorphic flows along the typical fibers of the submersion $(F₁, ..., F_\{j-1\}, F_\{j+1\}, ..., Fₙ)$, then the inverse map exists. Several equivalent versions of this main hypothesis are given.},
author = {Alvaro Bustinduy, Luis Giraldo, Jesús Muciño-Raymundo},
journal = {Colloquium Mathematicae},
keywords = {holomorphic foliations; Jacobian conjecture; non-singular complex polynomial vector fields},
language = {eng},
number = {2},
pages = {205-220},
title = {Vector fields from locally invertible polynomial maps in ℂⁿ},
url = {http://eudml.org/doc/283735},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Alvaro Bustinduy
AU - Luis Giraldo
AU - Jesús Muciño-Raymundo
TI - Vector fields from locally invertible polynomial maps in ℂⁿ
JO - Colloquium Mathematicae
PY - 2015
VL - 140
IS - 2
SP - 205
EP - 220
AB - Let (F₁,..., Fₙ): ℂⁿ → ℂⁿ be a locally invertible polynomial map. We consider the canonical pull-back vector fields under this map, denoted by ∂/∂F₁,...,∂/∂Fₙ. Our main result is the following: if n-1 of the vector fields $∂/∂F_{j}$ have complete holomorphic flows along the typical fibers of the submersion $(F₁, ..., F_{j-1}, F_{j+1}, ..., Fₙ)$, then the inverse map exists. Several equivalent versions of this main hypothesis are given.
LA - eng
KW - holomorphic foliations; Jacobian conjecture; non-singular complex polynomial vector fields
UR - http://eudml.org/doc/283735
ER -