Algebraic Integrability of Foliations of the Plane
Dynamical Systems
2007-05-23 v2 Complex Variables
Abstract
We give an algorithm to decide whether an algebraic plane foliation F has a rational first integral and to compute it in the affirmative case. The algorithm runs whenever we assume the polyhedrality of the cone of curves of the surface obtained after blowing-up the set B_F of infinitely near points needed to get the dicritical exceptional divisors of a minimal resolution of the singularities of F. This condition can be detected in several ways, one of them from the proximity relations in B_F and, as a particular case, it holds when the cardinality of B_F is less than 9.
Keywords
Cite
@article{arxiv.math/0511416,
title = {Algebraic Integrability of Foliations of the Plane},
author = {C. Galindo and F. Monserrat},
journal= {arXiv preprint arXiv:math/0511416},
year = {2007}
}