Algebraic integrability of foliations of the plane

[摘要] 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. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15