Let be a holomorphic foliation by curves on . We treat the case where the set 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 dans . Nous considérons le cas où l’ensemble 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.
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DOI : 10.5802/afst.1123
Gilcione Nonato Costa 1
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author = {Gilcione Nonato Costa},
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},
pages = {297--321},
year = {2006},
publisher = {Universit\'e Paul Sabatier, Toulouse},
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Gilcione Nonato Costa. Holomorphic foliations by curves on $\mathbb{P}^3$ with non-isolated singularities. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 15 (2006) no. 2, pp. 297-321. doi: 10.5802/afst.1123
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