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

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

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

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     title = {Holomorphic foliations in ${\mathbb {C}}{\mathbb {P}}(2)$ having an invariant algebraic curve},
     journal = {Annales de l'Institut Fourier},
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Cerveau, Dominique; Neto, Alcides Lins. Holomorphic foliations in ${\mathbb {C}}{\mathbb {P}}(2)$ having an invariant algebraic curve. Annales de l'Institut Fourier, Tome 41 (1991) no. 4, pp. 883-903. doi : 10.5802/aif.1278. https://aif.centre-mersenne.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). | 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

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