Foliations by curves with curves as singularities
Annales de l'Institut Fourier, Volume 64 (2014) no. 4, p. 1781-1805

Let be a holomorphic one-dimensional foliation on 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 and C i , assuming that 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.

Soit un feuilletage holomorphe unidimensionnel sur 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 et C i , en supposant que 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.

DOI : https://doi.org/10.5802/aif.2896
Classification:  32S65,  58K45
Keywords: holomorphic foliations, non-isolated singularities
@article{AIF_2014__64_4_1781_0,
     author = {Corr\^ea Jr, M. and Fern\'andez-P\'erez, A. and Nonato Costa, G. and Vidal Martins, R.},
     title = {Foliations by curves  with curves as singularities},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {4},
     year = {2014},
     pages = {1781-1805},
     doi = {10.5802/aif.2896},
     mrnumber = {3329679},
     zbl = {06387323},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_4_1781_0}
}
Corrêa Jr, M.; Fernández-Pérez, A.; Nonato Costa, G.; Vidal Martins, R. Foliations by curves  with curves as singularities. Annales de l'Institut Fourier, Volume 64 (2014) no. 4, pp. 1781-1805. doi : 10.5802/aif.2896. http://www.numdam.org/item/AIF_2014__64_4_1781_0/

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