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Vector fields from locally invertible polynomial maps in ℂⁿ

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Bustinduy A., Giraldo L., Muciño-Raymundo J.

Colloquium Mathematicum

2015

tom 140

nr 2

205-220

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Bustinduy A.

1 Giraldo L.

1 Muciño-Raymundo J.

1 2015

Wyniki wyszukiwania

Vector fields from locally invertible polynomial maps in ℂⁿ