Foliations in algebraic surfaces having a rational first integral.

García Zamora, Alexis. "Foliations in algebraic surfaces having a rational first integral.." Publicacions Matemàtiques 41.2 (1997): 357-373. <http://eudml.org/doc/41321>.

@article{GarcíaZamora1997,
abstract = {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.},
author = {García Zamora, Alexis},
journal = {Publicacions Matemàtiques},
keywords = {Geometría algebraica; Problema de Poincaré; Foliaciones; Análisis complejo; Ecuaciones diferenciales ordinarias; foliation; algebraic surface; Poincaré problem; rational surface; singularities},
language = {eng},
number = {2},
pages = {357-373},
title = {Foliations in algebraic surfaces having a rational first integral.},
url = {http://eudml.org/doc/41321},
volume = {41},
year = {1997},
}

TY - JOUR
AU - García Zamora, Alexis
TI - Foliations in algebraic surfaces having a rational first integral.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 2
SP - 357
EP - 373
AB - 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.
LA - eng
KW - Geometría algebraica; Problema de Poincaré; Foliaciones; Análisis complejo; Ecuaciones diferenciales ordinarias; foliation; algebraic surface; Poincaré problem; rational surface; singularities
UR - http://eudml.org/doc/41321
ER -