Differentiable equisingularity of holomorphic foliations

Mol, Rogério; Rosas, Rudy

doi:10.48550/arxiv.1611.03004

Cited by 2 publications

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“…Recently, second type foliations have been the object of some works. We should mention [10] -which deals with the "realization problem", that is, the existence of foliations with prescribed reduction of singularities and projective holonomy representations, [11] -which studies local polar invariants and applications to the study of the Poincaré problem for foliations -and [19] -where equisingularitiy properties are considered. Our main goal in this article is to give a characterization of second type foliations by means of residue-type indices, providing a generalization of Brunella's result.…”

Section: Introductionmentioning

confidence: 99%

Residue-type indices and holomorphic foliations

Fernández‐Pérez¹,

Mol²

2019

Annali Scuola Normale Superiore - Classe Di Scienze

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We investigate residue-type indices for germs of holomorphic foliations in the plane and characterize second type foliations -those not containing tangent saddlenodes in the reduction of singularities -by an expression involving the Baum-Bott, variation and polar excess indices. These local results are applied in the study of logarithmic foliations on compact complex surfaces.2010 Mathematics Subject Classification. 32S65, 37F75.

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Section: Introductionmentioning

confidence: 99%

Residue-type indices and holomorphic foliations

Fernández‐Pérez¹,

Mol²

2019

Annali Scuola Normale Superiore - Classe Di Scienze

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“…For instance, if g = 0 is a reduced equation for the set of separatrices of a non-dicritical foliation G, then G is second type if and only if ν 0 (G) = ν 0 (dg), where ν stands for the algebraic multiplicity. These properties are the key ingredients used in [16] in order to prove that second type foliations equivalent by C ∞ diffeomorphisms are equisingular.…”

Section: Introductionmentioning

confidence: 99%

Second type foliations of codimension one

Cuzzuol

Mol

2018

Bol. Soc. Mat. Mex.

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In this article, for holomorphic foliations of codimension one at (C 3 , 0), we define the family of second type foliations. This is formed by foliations having, in the reduction process by blow-up maps, only well oriented singularities, meaning that the reduction divisor does not contain weak separatrices of saddle-node singularities. We prove that the reduction of singularities of a non-dicritical foliation of second type coincides with the desingularization of its set of separatrices.

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Differentiable equisingularity of holomorphic foliations

Cited by 2 publications

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Residue-type indices and holomorphic foliations

Residue-type indices and holomorphic foliations

Second type foliations of codimension one

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