[Feuilletages par des courbes ayant des courbes comme singularités]
Soit un feuilletage holomorphe unidimensionnel sur , dont les composantes du lieu singulier sont des courbes et des points . On exprime le nombre de tels points , comptés avec leurs multiplicités, en termes des invariants de et , en supposant que est spécial le long des courbes . En supposant qu’il n’y a qu’une seule composante de de dimension non nulle, on obtient aussi des résultats lorsque le feuilletage est déterminé par ses lieux singuliers.
Let be a holomorphic one-dimensional foliation on such that the components of its singular locus are curves and points . We determine the number of , counted with multiplicities, in terms of invariants of and , assuming that is special along the . Allowing just one nonzero dimensional component on , we also prove results on when the foliation happens to be determined by its singular locus.
Keywords: holomorphic foliations, non-isolated singularities
Mot clés : feuilletages holomorphes, singularités non-isolées
@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},
pages = {1781--1805},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {64},
number = {4},
year = {2014},
doi = {10.5802/aif.2896},
zbl = {06387323},
mrnumber = {3329679},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2896/}
}
TY - JOUR AU - Corrêa Jr, M. AU - Fernández-Pérez, A. AU - Nonato Costa, G. AU - Vidal Martins, R. TI - Foliations by curves with curves as singularities JO - Annales de l'Institut Fourier PY - 2014 SP - 1781 EP - 1805 VL - 64 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2896/ DO - 10.5802/aif.2896 LA - en ID - AIF_2014__64_4_1781_0 ER -
%0 Journal Article %A Corrêa Jr, M. %A Fernández-Pérez, A. %A Nonato Costa, G. %A Vidal Martins, R. %T Foliations by curves with curves as singularities %J Annales de l'Institut Fourier %D 2014 %P 1781-1805 %V 64 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2896/ %R 10.5802/aif.2896 %G en %F 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, Tome 64 (2014) no. 4, pp. 1781-1805. doi : 10.5802/aif.2896. http://www.numdam.org/articles/10.5802/aif.2896/
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