An Improvement to Lagutinskii–Pereira Integrability Theorem

We give an improvement of an integrability theorem due to J. V. Pereira for holomorphic foliations of dimension one on complex manifolds. We give bounds for the degree and number of invariant reduced divisors contained in linear systems of projective manifolds. We construct examples of foliations on projective spaces with the maximum number of invariant hyperplanes. Also, in the appendix of this work we prove a Jouanolou–Ghys type theorem for one-dimensional foliations on compact complex manifolds.

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Published 19 August 2011