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Varietà complesse a struttura grassmanniana

Francesco Gherardelli (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We define and study the notions of connections and structures of grassmannian type on complex manifolds.

Vector fields from locally invertible polynomial maps in ℂⁿ

Alvaro Bustinduy, Luis Giraldo, Jesús Muciño-Raymundo (2015)

Colloquium Mathematicae

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 ( F , . . . , F j - 1 , F j + 1 , . . . , F ) , then the inverse map exists. Several equivalent versions of this main hypothesis are given.

Vector fields, invariant varieties and linear systems

Jorge Vitório Pereira (2001)

Annales de l’institut Fourier

We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criterion for the existence of rational first integrals of a given degree, bounds for the number of first integrals on families of vector fields, and a generalization of Darboux's criteria. We also provide a new proof of Gomez--Mont's result on foliations...

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