Foliations in algebraic surfaces having a rational first integral

Autores: Alexis García Zamora
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 41, Nº 2, 1997, págs. 357-373
Idioma: inglés
DOI: 10.5565/publmat_41297_03
Títulos paralelos:
- Foliaciones en superficies algebraicas que tienen un primera integral racional
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Resumen
- Given a foliation $\Cal F$ in an algebraic surface having a rational first integral a genus formula for the general solution is obtained. In the case $S=\Bbb P^2$ some new counter-examples to the classic formulation of the Poincaré problem are presented. If $S$ is a rational surface and $\Cal F$ has singularities of type $(1,1)$ or $(1,-1)$ we prove that the general solution is a non-singular curve.