Holomorphic foliations by curves on ${\mathbb{P}}^3$ with non-isolated singularities

Nonato Costa, Gilcione. "Holomorphic foliations by curves on $\mathbb{P}^3$ with non-isolated singularities." Annales de la faculté des sciences de Toulouse Mathématiques 15.2 (2006): 297-321. <http://eudml.org/doc/10000>.

@article{NonatoCosta2006,
abstract = {Let $\mathcal\{F\}$ be a holomorphic foliation by curves on $\mathbb\{P\}^3$. We treat the case where the set $\operatorname\{Sing\}(\mathcal\{F\})$ 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 $\mathcal\{F\}$, the multiplicity of $\mathcal\{F\}$ along the curves and the degree and genus of the curves.},
affiliation = {Departamento de Matemática - ICEX - UFMG. Cep 30123-970 - Belo Horizonte, Brazil.},
author = {Nonato Costa, Gilcione},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {holomorphic foliation; singularities; multiplicity; tangent bundle; Chern classes},
language = {eng},
number = {2},
pages = {297-321},
publisher = {Université Paul Sabatier, Toulouse},
title = {Holomorphic foliations by curves on $\mathbb\{P\}^3$ with non-isolated singularities},
url = {http://eudml.org/doc/10000},
volume = {15},
year = {2006},
}

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
PB - Université Paul Sabatier, Toulouse
VL - 15
IS - 2
SP - 297
EP - 321
AB - Let $\mathcal{F}$ be a holomorphic foliation by curves on $\mathbb{P}^3$. We treat the case where the set $\operatorname{Sing}(\mathcal{F})$ 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 $\mathcal{F}$, the multiplicity of $\mathcal{F}$ along the curves and the degree and genus of the curves.
LA - eng
KW - holomorphic foliation; singularities; multiplicity; tangent bundle; Chern classes
UR - http://eudml.org/doc/10000
ER -