Preprint A07/2001
Invariant Hypersurfaces for Positive Characteristic Vector Fields
Jorge Vitório Pereira
Keywords: Invariant hypersurfaces | derivations | positive characteristic | vector fields
We show that a generic vector field on an affine space of positive characteristic admits an invariant algebraic hypersurface. This is in sharp contrast with the characteristic zero case where Jouanolou's Theorem says that a generic vector field on the complex plane does not admit any invariant algebraic curve.