Jacobian curve of singular foliations
[Courbe jacobienne de feuilletages singuliers]
Corral, Nuria1
1 Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda. de los Castros s/n, 39005 – Santander (Spain)
Annales de l'Institut Fourier, Online first, 61 p.

Nous décrivons des propriétés topologiques de la courbe jacobienne 𝒥 ℱ,𝒢 de deux feuilletages ℱ et 𝒢 en termes des invariants associés aux feuilletages. Le resultat principal donne une décomposition de la courbe jacobienne 𝒥 ℱ,𝒢 qui dépend de la similitude des feuilletages ℱ et 𝒢. Cette similitude entre les feuilletages est codifiée en termes des indices de Camacho–Sad des feuilletages avec la notion de point ou diviseur colinéaire. Notre approche permet de récupérer les résultats concernant la factorisation de la courbe jacobienne de deux courbes planes et de la courbe polaire d’une courbe ou d’un feuilletage.

Topological properties of the jacobian curve 𝒥 ℱ,𝒢 of two foliations ℱ and 𝒢 are described in terms of invariants associated to the foliations. The main result gives a decomposition of the jacobian curve 𝒥 ℱ,𝒢 which depends on how similar are the foliations ℱ and 𝒢. The similarity between foliations is codified in terms of the Camacho–Sad indices of the foliations with the notion of collinear point or divisor. Our approach allows to recover the results concerning the factorization of the jacobian curve of two plane curves and of the polar curve of a curve or a foliation.

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DOI : 10.5802/aif.3665
Classification : 32S65, 32S50, 14H20
Keywords: Jacobian curve, singular foliation, polar curve, Camacho–Sad index, equisingularity data.
Mot clés : Courbe jacobienne, feuilletage singulier, courbe polaire, indice de Camacho–Sad, type d’équisingularité.
Corral, Nuria 1

1 Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda. de los Castros s/n, 39005 – Santander (Spain) 
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Corral, Nuria. Jacobian curve of singular foliations. Annales de l'Institut Fourier, Online first, 61 p.

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