# Foliations in algebraic surfaces having a rational first integral.

Publicacions Matemàtiques (1997)

- Volume: 41, Issue: 2, page 357-373
- ISSN: 0214-1493

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topGarcía 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 -

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