no. 4
Foliations by curves with curves as singularities
[Feuilletages par des courbes ayant des courbes comme singularités]
Corrêa Jr, M.1 ; Fernández-Pérez, A.1 ; Nonato Costa, G.1 ; Vidal Martins, R.1
1 ICEx - UFMG Departamento de Matemática Av. Antônio Carlos 6627 30123-970 Belo Horizonte MG (Brazil)
Annales de l'Institut Fourier, Tome 64 (2014) no. 4, pp. 1781-1805.

Soit ℱ un feuilletage holomorphe unidimensionnel sur ℙ n , dont les composantes du lieu singulier Σ sont des courbes C i et des points p j . On exprime le nombre de tels points p j , comptés avec leurs multiplicités, en termes des invariants de ℱ et C i , en supposant que ℱ est spécial le long des courbes C i . En supposant qu’il n’y a qu’une seule composante de Σ de dimension non nulle, on obtient aussi des résultats lorsque le feuilletage est déterminé par ses lieux singuliers.

Let ℱ be a holomorphic one-dimensional foliation on ℙ n such that the components of its singular locus Σ are curves C i and points p j . We determine the number of p j , counted with multiplicities, in terms of invariants of ℱ and C i , assuming that ℱ is special along the C i . Allowing just one nonzero dimensional component on Σ, we also prove results on when the foliation happens to be determined by its singular locus.

DOI : 10.5802/aif.2896
Classification : 32S65, 58K45
Keywords: holomorphic foliations, non-isolated singularities
Mot clés : feuilletages holomorphes, singularités non-isolées

Corrêa Jr, M. 1 ; Fernández-Pérez, A. 1 ; Nonato Costa, G. 1 ; Vidal Martins, R. 1

1 ICEx - UFMG Departamento de Matemática Av. Antônio Carlos 6627 30123-970 Belo Horizonte MG (Brazil) 
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     title = {Foliations by curves  with curves as singularities},
     journal = {Annales de l'Institut Fourier},
     pages = {1781--1805},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Corrêa Jr, M.; Fernández-Pérez, A.; Nonato Costa, G.; Vidal Martins, R. Foliations by curves  with curves as singularities. Annales de l'Institut Fourier, Tome 64 (2014) no. 4, pp. 1781-1805. doi : 10.5802/aif.2896. https://aif.centre-mersenne.org/articles/10.5802/aif.2896/

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