Displaying similar documents to “The C 1 invariance of the algebraic multiplicity of a holomorphic vector field”

Finite determinacy of dicritical singularities in ( 2 , 0 )

Gabriel Calsamiglia-Mendlewicz (2007)

Annales de l’institut Fourier

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For germs of singularities of holomorphic foliations in ( 2 , 0 ) which are regular after one blowing-up we show that there exists a functional analytic invariant (the transverse structure to the exceptional divisor) and a finite number of numerical parameters that allow us to decide whether two such singularities are analytically equivalent. As a result we prove a formal-analytic rigidity theorem for this kind of singularities.

A Fatou-Julia decomposition of transversally holomorphic foliations

Taro Asuke (2010)

Annales de l’institut Fourier

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A Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one was given by Ghys, Gomez-Mont and Saludes. In this paper, we propose another decomposition in terms of normal families. Two decompositions have common properties as well as certain differences. It will be shown that the Fatou sets in our sense always contain the Fatou sets in the sense of Ghys, Gomez-Mont and Saludes and the inclusion is strict in some examples. This property is important when...

A note on M. Soares’ bounds

Eduardo Esteves, Israel Vainsencher (2006)

Annales de l’institut Fourier

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We give an intersection theoretic proof of M. Soares’ bounds for the Poincaré-Hopf index of an isolated singularity of a foliation of ℂℙ n .

On Halphen’s Theorem and some generalizations

Alcides Lins Neto (2006)

Annales de l’institut Fourier

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Let M n be a germ at 0 m of an irreducible analytic set of dimension n , where n 2 and 0 is a singular point of M . We study the question: when does there exist a germ of holomorphic map φ : ( n , 0 ) ( M , 0 ) such that φ - 1 ( 0 ) = { 0 } ? We prove essentialy three results. In Theorem 1 we consider the case where M is a quasi-homogeneous complete intersection of k polynomials F = ( F 1 , ... , F k ) , that is there exists a linear holomorphic vector field X on m , with eigenvalues λ 1 , ... , λ m + such that X ( F T ) = U · F T , where U is a k × k matrix with entries in 𝒪 m . We prove that if...