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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

Official URL: http://journals.impan.gov.pl/cgi-bin/cm/pdf?cm140-2-04

## 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.

Item Type: | Article |
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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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