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On the density of algebraic foliations without algebraic invariant sets
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17. Mai 2006
Abstract
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.
Received: 2003-08-27
Revised: 2005-03-16
Published Online: 2006-05-17
Published in Print: 2006-05-01
© Walter de Gruyter
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Artikel in diesem Heft
- Traces of CM values of modular functions
- Représentations semi-stables de torsion dans le cas er < p − 1
- Zero cycles on a threefold with isolated singularities
- On the density of algebraic foliations without algebraic invariant sets
- Compactness of solutions to some geometric fourth-order equations
- Relative cohomology with respect to a Lefschetz pencil
- There are genus one curves of every index over every number field
- The uniqueness of Cuntz-Krieger type algebras
Artikel in diesem Heft
- Traces of CM values of modular functions
- Représentations semi-stables de torsion dans le cas er < p − 1
- Zero cycles on a threefold with isolated singularities
- On the density of algebraic foliations without algebraic invariant sets
- Compactness of solutions to some geometric fourth-order equations
- Relative cohomology with respect to a Lefschetz pencil
- There are genus one curves of every index over every number field
- The uniqueness of Cuntz-Krieger type algebras
