Preprint A162/2002
On the density of algebraic foliations without algebraic invariant sets

Jorge VitÃ³rio Pereira | Coutinho, Severino Collier

**Keywords: **
algebraic foliation | invariant subvarieties

Let $X$ be a complex projective variety of dimension greater than or equal to $2$, and let $k\gg 0$ be an integer. We prove that a generic global section of the twisted tangent
sheaf $\Theta_X(k)$ gives rise to a foliation of $X$ without any proper algebraic invariant subvarieties of non-zero dimension. We also extend this result to fields of $m$-vectors over $X$.