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

Gilcione Nonato Costa^{[1]}

- [1] Departamento de Matemática - ICEX - UFMG. Cep 30123-970 - Belo Horizonte, Brazil.

Annales de la faculté des sciences de Toulouse Mathématiques (2006)

- Volume: 15, Issue: 2, page 297-321
- ISSN: 0240-2963

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topNonato 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 -

## References

top- P. Baum, R. Bott, On the zeros of meromorphic vector-fields, Essays on Topology and Related topics (1970), 29-47, Springer-Verlag, Berlin Zbl0193.52201MR261635
- R. Bott, L. W. Tu, Differential Forms in Algebraic Topology, Graduate Texts in Mathematics 82 (1982), Springer Zbl0496.55001MR658304
- W. Fulton, Intersection Theory, (1984), Springer-Verlag, Berlin Heidelberg Zbl0541.14005MR732620
- X. Gómez-Mont, Holomorphic foliations in ruled surfaces, Trans. American Mathematical Society 312 (1989), 179-201 Zbl0669.57012MR983870
- P. Griffiths, J. Harris, Principles of Algebraic Geometry, (1994), John Wiley & Sons, Inc. Zbl0836.14001MR1288523
- R. Hartshorne, Algebraic Geometry, (1977), Springer-Verlag, New York Inc Zbl0367.14001MR463157
- I. R. Porteous, Blowing up Chern class, Proc. Cambridge Phil. Soc. 56 (1960), 118-124 Zbl0166.16701MR121813
- F. Sancho, Number of singularities of a foliation on ${\mathbb{P}}^{n}$, Proceedings of the American Mathematical Society 130 (2001), 69-72 Zbl0987.32015MR1855621
- T. Suwa, Indices of vector fields and residues of singular holomorphic foliation, (1998), Hermann Zbl0910.32035MR1649358

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