Holomorphic foliations of degree four on the complex projective space

2022/08/08 by Fernández-Pérez, Arturo, Maia, Vângellis Sagnori
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.04092

Abstract

In this paper, we study holomorphic foliations of degree four on complex projective space ℙⁿ, where n≥ 3, with a special focus on obtaining a structural theorem for these foliations. Furthermore, for a foliation F of degree d≥ 4 with a sufficiently high k^th-jet, we prove that either F is transversely affine outside a compact hypersurface, or F is transversely projective outside a compact hypersurface, or F is the pull-back of a foliation on F² by a rational map.

Related

• Foliations on complex projective surfaces
• Transversely projective holomorphic foliations with singularities
• Convex foliations of degree 4 on the complex projective plane
• Dynamics of Singular Holomorphic Foliations on the Complex Projective Plane
• Holomorphic vector fields tangent to foliations in dimension three