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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.24 no.2 Antofagasta Aug. 2005

http://dx.doi.org/10.4067/S0716-09172005000200006 

 

Proyecciones
Vol. 24, No 2, pp. 175-179, August 2005.
Universidad Católica del Norte
Antofagasta - Chile

 

ON FOLIATIONS WITH RATIONAL FIRST INTEGRAL

 

SERGIO LICANIC

Universidade Federal Fluminense, Brazil

Correspondencia a :


ABSTRACT

We use the Kodaira’s classification of relatively minimal elliptic fibrations to prove that a holomorphic foliation in CP2 with a dicritical compact elliptic curve has rational first integral.

Keywords : Compact complex surfaces, Holomorphic foliation, Invariant compact curves.

AMS classification : 34A20-58F18


 

REFERENCES

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[5] D. Cerveau and A. Lins Neto, Holomorphic foliation in CP2 having an invariant algebraic curve, Ann. Inst. Fourier, Grenoble 41, 4, pp. 883—903, (1991).        [ Links ]

[6] A. Lins Neto Some examples for the Poincaré and Painlevé problems, Ann. Sci. École Norm. Sup. (4) 35, No. 2, pp. 231—266, (2002).        [ Links ]

[7] S. Licanic, An upper bound for the total sum of the Baum-Bott indexes of a holomorphic foliation and the Poincare Problem, Hokkaido Mathematical Journal Vol. 33, No.3, October, (2004).        [ Links ]

[8] H. Poincaré Sur líntégration algébrique des équations différentielles, C. R. Acad. Sci. 112, pp. 761—764, (1891).        [ Links ]

[9] H. Poincaré Sur l´íntégration algébrique des équations différentielles du premier ordre et du premier degré, Rend. Circ. Mat. Palermo 5, pp. 161—191, (1891).        [ Links ]

[10] H. Poincaré Sur l´íntégration algébrique des équations différentielles du premier ordre et du premier degré , Rend. Circ. Mat. Palermo 11, pp. 193—239, (1897).        [ Links ]

Received : June 2004. Accepted : August 2005

Sergio Licanic

Dep. de Matemática Aplicada
Universidade Federal Fluminense UFF
Rua Mario Santos Braga s/n
Pra¸ca do Valonginho-Centro-Niteroi
CEP: 24020-140
Brazil
e-mail : ser@impa.br

 

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