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arXiv · 2102.10608

Codimension one foliations of degree three on projective spaces

Raphael Constant da Costa·Ruben Lizarbe·Jorge Vitório Pereira
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Abstract

We establish a structure theorem for degree three codimension one foliations on projective spaces of dimension $n\ge 3$, extending a result by Loray, Pereira, and Touzet for degree three foliations on $\mathbb P^3$. We show that the space of codimension one foliations of degree three on $\mathbb{P}^n$, $n\ge 3$, 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.

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Raphael Constant da Costa, Ruben Lizarbe, Jorge Vitório Pereira. 2021-02-21. Codimension one foliations of degree three on projective spaces. https://arxiv.org/abs/2102.10608

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