Displaying similar documents to “Finite determinacy of dicritical singularities in ( ℂ 2 , 0 ) ”

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 ∈ ℂ 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 : ( ℂ 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 ℂ m , with eigenvalues λ 1 , ... , λ m ∈ ℚ + such that X ( F T ) = U · F T , where U is a k × k matrix with entries in 𝒪 m . We prove that if...

Small divisors and large multipliers

Boele Braaksma, Laurent Stolovitch (2007)

Annales de l’institut Fourier

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We study germs of singular holomorphic vector fields at the origin of ℂ n of which the linear part is 1 -resonant and which have a polynomial normal form. The formal normalizing diffeomorphism is usually divergent at the origin but there exists holomorphic diffeomorphisms in some “sectorial domains” which transform these vector fields into their normal form. In this article, we study the interplay between the small divisors phenomenon and the Gevrey character of the sectorial normalizing...