Holomorphic foliations in (2) having an invariant algebraic curve
Annales de l'Institut Fourier, Volume 41 (1991) no. 4, pp. 883-903.

We give estimations for the degree of separatrices of algebraic foliations in CP(2).

Nous estimons le degré des séparatrices d’un feuilletage algébrique de CP(2) en fonction du degré du feuilletage.

@article{AIF_1991__41_4_883_0,
     author = {Cerveau, Dominique and Neto, Alcides Lins},
     title = {Holomorphic foliations in ${\mathbb {C}}{\mathbb {P}}(2)$ having an invariant algebraic curve},
     journal = {Annales de l'Institut Fourier},
     pages = {883--903},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {41},
     number = {4},
     year = {1991},
     doi = {10.5802/aif.1278},
     mrnumber = {93b:32050},
     zbl = {0734.34007},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1278/}
}
TY  - JOUR
AU  - Cerveau, Dominique
AU  - Neto, Alcides Lins
TI  - Holomorphic foliations in ${\mathbb {C}}{\mathbb {P}}(2)$ having an invariant algebraic curve
JO  - Annales de l'Institut Fourier
PY  - 1991
SP  - 883
EP  - 903
VL  - 41
IS  - 4
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.1278/
DO  - 10.5802/aif.1278
LA  - en
ID  - AIF_1991__41_4_883_0
ER  - 
%0 Journal Article
%A Cerveau, Dominique
%A Neto, Alcides Lins
%T Holomorphic foliations in ${\mathbb {C}}{\mathbb {P}}(2)$ having an invariant algebraic curve
%J Annales de l'Institut Fourier
%D 1991
%P 883-903
%V 41
%N 4
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/aif.1278/
%R 10.5802/aif.1278
%G en
%F AIF_1991__41_4_883_0
Cerveau, Dominique; Neto, Alcides Lins. Holomorphic foliations in ${\mathbb {C}}{\mathbb {P}}(2)$ having an invariant algebraic curve. Annales de l'Institut Fourier, Volume 41 (1991) no. 4, pp. 883-903. doi : 10.5802/aif.1278. http://www.numdam.org/articles/10.5802/aif.1278/

[1] H. Cartan, Sur le premier problème de Cousin, C.R. Acad. Sc., 207 (1938), 558-560. | JFM | Zbl

[2] D. Cerveau, J. F. Mattei, Formes intégrables holomorphes singulières, Asterisque, 97 (1983). | Numdam | MR | Zbl

[3] J. C. Jouanolou, Equations de Pfaff algébriques, Lect. Notes in Math., 708 (1979). | MR | Zbl

[4] A. Lins Neto, Algebraic solutions of polynomial differential equations and foliations in dimension two, in Holomorphic dynamics, Lect. Notes in Math., 1345 (1988). | MR | Zbl

[5] Poincaré, Sur l'intégration algébrique des équations diff. du 1er ordre, Rendiconti del circolo matematico di Palermo, t. 11, p. 193-239. | JFM

[6] K. Saïto, On a generalisation of the Rham Lemma, Ann. Inst. Fourier, 26-2 (1976), 165-170. | Numdam | MR | Zbl

[7] K. Saïto, Quasi homogene isolierte singularitäten von Hyperflächen, Invent. Math., 14 (1971), 123-142. | MR | Zbl

[8] C. Camacho, A. Lins Neto, P. Sad, Topological invariants and equidesingularization for holomorphic vector fields, J. of Diff. Geometry, vol. 20, n° 1 (1984), 143-174. | MR | Zbl

Cited by Sources: