Vector fields from locally invertible polynomial maps in ℂⁿ
Alvaro Bustinduy ; Luis Giraldo ; Jesús Muciño-Raymundo
Colloquium Mathematicae, Tome 139 (2015), p. 205-220 / Harvested from The Polish Digital Mathematics Library
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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 ∂/∂Fj have complete holomorphic flows along the typical fibers of the submersion (F₁,...,Fj-1,Fj+1,...,Fₙ), then the inverse map exists. Several equivalent versions of this main hypothesis are given.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:283735 
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     author = {Alvaro Bustinduy and Luis Giraldo and Jes\'us Muci\~no-Raymundo},
     title = {Vector fields from locally invertible polynomial maps in Cn},
     journal = {Colloquium Mathematicae},
     volume = {139},
     year = {2015},
     pages = {205-220},
     zbl = {1335.14014},
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Alvaro Bustinduy; Luis Giraldo; Jesús Muciño-Raymundo. Vector fields from locally invertible polynomial maps in ℂⁿ. Colloquium Mathematicae, Tome 139 (2015) pp. 205-220. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-2-4/