# Vector fields from locally invertible polynomial maps in ℂⁿ

Alvaro Bustinduy; Luis Giraldo; Jesús Muciño-Raymundo

Colloquium Mathematicae (2015)

- Volume: 140, Issue: 2, page 205-220
- ISSN: 0010-1354

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topAlvaro 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 -

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