Non-algebraicity of foliations via reduction modulo 2
Abstract
We investigate the non-algebraicity of foliations of rank one on [Formula: see text]. We present a criterion to show that such a foliation has no algebraic invariant curves, using a method of reduction modulo 2. Finally, using this criterion we give a new proof that the Jouanolou foliation of odd degree has no algebraic invariant curves. We also present other classes of foliations without algebraic invariant curves.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Algebraic Geometry and Number Theory
Polynomial and algebraic computation
Publication details
- Journal / source
- Journal of Algebra and Its Applications
- Publisher
- World Scientific Pub Co Pte Ltd
- Publication date
- 8 May 2026
- Language
- EN