Degree-one foliations on complete intersections

2025/07/10 by Mateus Gomes Figueira, Mateus Figueira, Crislaine Kuster +6
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #math.CV

paper · pdf · doi:10.48550/arxiv.2507.08090

openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for any smooth hypersurface of dimension at least three that is not a quadric threefold. The proof of these results follows essentially from a more general structure theorem for foliations on manifolds covered by lines.

Citations

• The space of foliations on projective spaces in positive characteristic
• Codimension-one foliations on adjoint varieties
• Extensions and restrictions of holomorphic foliations
• Codimension one foliations on homogeneous varieties
• Codimension one foliations of degree three on projective spaces
• Rational pullbacks of toric foliations
• On Fano foliations
• Foliations with trivial canonical bundle on Fano 3-folds
• Feuilletages et actions de groupes sur les espaces projectifs

Related

• Codimension one foliations of degree three on projective spaces
• Transversely Lie holomorphic foliations on projective spaces
• Unlikely intersections of codimension one foliations
• Codimension-one foliations on adjoint varieties
• Codimension one foliations with trivial canonical class on singular spaces II