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.

Anexos:

• jpaa.pdf