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.
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.
@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},
pages = {297--321},
publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 15},
number = {2},
year = {2006},
doi = {10.5802/afst.1123},
zbl = {1129.32018},
mrnumber = {2244219},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/afst.1123/}
}
TY - JOUR
AU - Nonato Costa, Gilcione
TI - Holomorphic foliations by curves on $\mathbb{P}^3$ with non-isolated singularities
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2006
SP - 297
EP - 321
VL - 15
IS - 2
PB - Université Paul Sabatier, Institut de mathématiques
PP - Toulouse
UR - http://archive.numdam.org/articles/10.5802/afst.1123/
DO - 10.5802/afst.1123
LA - en
ID - AFST_2006_6_15_2_297_0
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%0 Journal Article
%A Nonato Costa, Gilcione
%T Holomorphic foliations by curves on $\mathbb{P}^3$ with non-isolated singularities
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
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%I Université Paul Sabatier, Institut de mathématiques
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Nonato Costa, Gilcione. 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. http://archive.numdam.org/articles/10.5802/afst.1123/
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