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arXiv · 2608.26470

The Geometry of the Exceptional Component of Degree Two Foliations on $\mathbb{P}^3$

Claudia R. Alcántara·Dominique Cerveau
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Abstract

We study the exceptional component of the space $\mathbb{F}(2,\mathbb{P}^3)$, of codimension-one foliations of degree two on $\mathbb{P}^3$. We describe the geometry of its boundary and prove that it has four irreducible components, all of dimension $12$. Three of these components contain a dense subset given by the orbit of a logarithmic foliation of type $(1,1,2)$, while the fourth contains a family of pull-back type foliations from $\mathbb{P}^2$ whose orbits have dimension $11$.

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Claudia R. Alcántara, Dominique Cerveau. 2026-08-26. The Geometry of the Exceptional Component of Degree Two Foliations on $\mathbb{P}^3$. https://arxiv.org/abs/2608.26470

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