The index of a holomorphic flow with an isolated singularity

Gómez-Mont, Xavier; Seade, José; Verjovsky, Alberto

doi:10.1007/bf01445237

Cited by 92 publications

(79 citation statements)

References 20 publications

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“…Two foliations on P 2 which are topological equivalent have the same degree. In fact, the first Chern class of the tangent bundle of a foliation is invariant by topological equivalences (see [8] This result leads to the following question:…”

Section: The Genus Of the Polar Curvementioning

confidence: 99%

The polar curve of a foliation on ℙ 2

Mol¹

2011

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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Section: The Genus Of the Polar Curvementioning

confidence: 99%

The polar curve of a foliation on ℙ 2

Mol¹

2011

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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“…This index, defined in [6,7], is an analogue of the GSV-index for vector fields, introduced in [11,20]. It is proved in [7], Proposition 3, that this index equals the number of zeroes, counted with multiplicities, of any extension of ω to a Milnor fibre…”

Section: Indices Of 1-formsmentioning

confidence: 99%

Homological Index for 1-Forms and a Milnor Number for Isolated Singularities

2004

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Abstract. We introduce a notion of a homological index of a holomorphic 1-form on a germ of a complex analytic variety with an isolated singularity, inspired by X. Gómez-Mont and G.-M. Greuel. For isolated complete intersection singularities it coincides with the index defined earlier by two of the authors. Subtracting from this index another one, called radial, we get an invariant of the singularity which does not depend on the 1-form. For isolated complete intersection singularities this invariant coincides with the Milnor number. We compute this invariant for arbitrary curve singularities and compare it with the Milnor number introduced by R.-O. Buchweitz and G.-M. Greuel for such singularities.

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“…In order to prove Theorem 1.1 we show that the algebraic multiplicity of F depends on the Chern class of the tangent bundle of F 0 . To relate the Chern classes of the tangent bundles of F 0 and F 0 we use the following theorem (see [7]). …”

Section: -Suppose That H Extends To the Divisor π −1 (0) As A Homeomomentioning

confidence: 99%

The C^1 invariance of the algebraic multiplicity of a holomorphic vector field

Rosas¹

2010

Ann. inst. Fourier

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The index of a holomorphic flow with an isolated singularity

Cited by 92 publications

References 20 publications

The polar curve of a foliation on ℙ 2

The polar curve of a foliation on ℙ 2

Homological Index for 1-Forms and a Milnor Number for Isolated Singularities

The C^1 invariance of the algebraic multiplicity of a holomorphic vector field

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