Holomorphic foliations by curves on 3 with non-isolated singularities
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 2, p. 297-321

Let be a holomorphic foliation by curves on 3 . We treat the case where the set Sing() consists of disjoint regular curves and some isolated points outside of them. In this situation, using Baum-Bott’s formula and Porteuos’theorem, we determine the number of isolated singularities, counted with multiplicities, in terms of the degree of , the multiplicity of along the curves and the degree and genus of the curves.

Soit un feuilletage holomorphe de dimension 1 dans 3 . Nous considérons le cas où l’ensemble Sing() est formé par des courbes lisses et disjointes et quelques points isolés en dehors de ces courbes. Dans cette situation, en employant la formule de Baum-Bott et le théorème de Porteous, nous déterminons le nombre de singularités isolées, comptées avec multiplicités, en fonction du degré de , de la multiplicité de le long des courbes et du degré et du genre des courbes.

@article{AFST_2006_6_15_2_297_0,
     author = {Nonato Costa, Gilcione},
     title = {Holomorphic foliations by curves on $\mathbb{P}^3$ with non-isolated singularities},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 15},
     number = {2},
     year = {2006},
     pages = {297-321},
     doi = {10.5802/afst.1123},
     mrnumber = {2244219},
     zbl = {1129.32018},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2006_6_15_2_297_0}
}
Nonato Costa, Gilcione. Holomorphic foliations by curves on $\mathbb{P}^3$ with non-isolated singularities. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 15 (2006) no. 2, pp. 297-321. doi : 10.5802/afst.1123. http://www.numdam.org/item/AFST_2006_6_15_2_297_0/

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