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S. C Coutinho, J. V Pereira

On the density of algebraic foliations without algebraic invariant sets

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.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2006, 05/2006
Pages: 117 - 135

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