Algebraic Integrability of Foliations of the Plane

Details Algebraic Integrability of Foliations of the Plane Algebraic Integrability of Foliations of the Plane

2005-11-16

arxiv.org/abs/math/0511416v2

Mathematics

Dynamical Systems

Scientific paper

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.

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