Holomorphic foliations in ( 2 ) having an invariant algebraic curve

Dominique Cerveau; Alcides Lins Neto

Annales de l'institut Fourier (1991)

  • Volume: 41, Issue: 4, page 883-903
  • ISSN: 0373-0956

Abstract

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

How to cite

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Cerveau, Dominique, and Neto, Alcides Lins. "Holomorphic foliations in ${\mathbb {C}}{\mathbb {P}}(2)$ having an invariant algebraic curve." Annales de l'institut Fourier 41.4 (1991): 883-903. <http://eudml.org/doc/74943>.

@article{Cerveau1991,
abstract = {We give estimations for the degree of separatrices of algebraic foliations in $\{\bf CP\}(2)$.},
author = {Cerveau, Dominique, Neto, Alcides Lins},
journal = {Annales de l'institut Fourier},
keywords = {holomorphic foliations; invariant algebraic curve; separatrices; algebraic foliations},
language = {eng},
number = {4},
pages = {883-903},
publisher = {Association des Annales de l'Institut Fourier},
title = {Holomorphic foliations in $\{\mathbb \{C\}\}\{\mathbb \{P\}\}(2)$ having an invariant algebraic curve},
url = {http://eudml.org/doc/74943},
volume = {41},
year = {1991},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 41
IS - 4
SP - 883
EP - 903
AB - We give estimations for the degree of separatrices of algebraic foliations in ${\bf CP}(2)$.
LA - eng
KW - holomorphic foliations; invariant algebraic curve; separatrices; algebraic foliations
UR - http://eudml.org/doc/74943
ER -

References

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  1. [1] H. CARTAN, Sur le premier problème de Cousin, C.R. Acad. Sc., 207 (1938), 558-560. Zbl0019.31503JFM64.0323.01
  2. [2] D. CERVEAU, J. F. MATTEI, Formes intégrables holomorphes singulières, Asterisque, 97 (1983). Zbl0545.32006MR86f:58006
  3. [3] J. C. JOUANOLOU, Equations de Pfaff algébriques, Lect. Notes in Math., 708 (1979). Zbl0477.58002MR81k:14008
  4. [4] A. LINS NETO, Algebraic solutions of polynomial differential equations and foliations in dimension two, in Holomorphic dynamics, Lect. Notes in Math., 1345 (1988). Zbl0677.58036MR90c:58142
  5. [5] POINCARÉ, Sur l'intégration algébrique des équations diff. du 1er ordre, Rendiconti del circolo matematico di Palermo, t. 11, p. 193-239. JFM28.0292.01
  6. [6] K. SAÏTO, On a generalisation of the Rham Lemma, Ann. Inst. Fourier, 26-2 (1976), 165-170. Zbl0338.13009MR54 #1276
  7. [7] K. SAÏTO, Quasi homogene isolierte singularitäten von Hyperflächen, Invent. Math., 14 (1971), 123-142. Zbl0224.32011MR45 #3767
  8. [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. Zbl0576.32020MR86d:58080

Citations in EuDML Documents

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  1. Henryk Żołądek, On algebraic solutions of algebraic Pfaff equations
  2. Olivier Ripoll, Julien Sebag, Tissus du plan et polynômes de Darboux
  3. S. C. Coutinho, A constructive proof of the Density of Algebraic Pfaff Equations without Algebraic Solutions
  4. Alcides Lins Neto, Some examples for the Poincaré and Painlevé problems
  5. A. Lins Neto, P. Sad, B. Scárdua, On topological rigidity of projective foliations
  6. B. Azevedo Scárdua, Transversely affine and transversely projective holomorphic foliations

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