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Publication Date:
May 2006
ISSN:
1435-5345
DOI:
10.1515/CRELLE.2006.037

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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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On the density of algebraic foliations without algebraic invariant sets

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Citation Information: Journal fur die reine und angewandte Mathematik (Crelles Journal). Volume 2006, Issue 594, Pages 117–135, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2006.037, May 2006

Publication History:
Received:
2003-08-27
Revised:
2005-03-16
Published Online:
2006-05-17

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.

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