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On the density of algebraic foliations without algebraic invariant sets

2006; De Gruyter; Volume: 2006; Issue: 594 Linguagem: Inglês

10.1515/crelle.2006.037

1435-5345

S. C. Coutinho, Jorge Vitório Pereira,

Meromorphic and Entire Functions

Let X be a smooth complex projective variety of dimension greater than or equal to 2, L an ample line bundle and k ≫ 0 an integer. We prove that a very generic global section of the twisted tangent sheaf gives rise to a foliation of X without any proper algebraic invariant subvarieties of nonzero dimension. As a corollary we obtain a dynamical characterization of ampleness for line bundles over smooth projective surfaces.