Vector fields from locally invertible polynomial maps in Cn



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Bustinduy, Álvaro and Giraldo Suárez, Luis and Muciño Raymundo, Jesús (2015) Vector fields from locally invertible polynomial maps in Cn. Colloquium Mathematicum, 140 (2). pp. 205-220. ISSN 0010-1354

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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.

Item Type:Article
Uncontrolled Keywords:Holomorphic foliations; Jacobian conjecture; non-singular complex polynomial vector fields
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:32895
Deposited On:26 Aug 2015 08:23
Last Modified:12 Dec 2018 15:12

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