2021/02/21 by Raphael Constant da Costa, da Costa, Raphael Constant, Ruben Lizarbe +3 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2102.10608
We establish a structure theorem for degree three codimension one foliations on projective spaces of dimension n≥ 3, extending a result by Loray, Pereira, and Touzet for degree three foliations on \mathbb P3. We show that the space of codimension one foliations of degree three on ℙn, n≥ 3, has exactly 18 distinct irreducible components parameterizing foliations without rational first integrals, and at least 6 distinct irreducible components parameterizing foliations with rational first integrals.