Type: Article

Vector fields from locally invertible polynomials maps in Cn

Bustinduy, Alvaro; Giraldo, Luis; Muciño-Raymundo, Jesús;

Abstract:

Let (F-1, . . . , F-n) : C-n -> C-n be a locally invertible polynomial map. We consider the canonical pull-back vector fields under this map, denoted by partial derivative/partial derivative F-1, . . . , partial derivative/partial derivative F-n. Our main result is the following: if n - 1 of the vector fields partial derivative/partial derivative F-j have complete holomorphic flows along the typical fibers of the submersion (F-1,. . . , Fj-1; F-j+1,F- . . . , F-n), then the inverse map exists. Several equivalent versions of this main hypothesis are given.