Given a foliation F in an algebraic surface having a rational first integral a genus formula for the general solution is obtained. In the case S = P2 some new counter-examples to the classic formulation of the Poincaré problem are presented. If S is a rational surface and F has singularities of type (1, 1) or (1,-1) we prove that the general solution is a non-singular curve.
@article{urn:eudml:doc:41321,
title = {Foliations in algebraic surfaces having a rational first integral.},
journal = {Publicacions Matem\`atiques},
volume = {41},
year = {1997},
pages = {357-373},
mrnumber = {MR1485488},
zbl = {0910.32039},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41321}
}
García Zamora, Alexis. Foliations in algebraic surfaces having a rational first integral.. Publicacions Matemàtiques, Tome 41 (1997) pp. 357-373. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41321/