Structural stability of the Jouanolou foliations in every degree

Sahil Gehlawat

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arXiv · 2609.35597

Structural stability of the Jouanolou foliations in every degree

Sahil Gehlawat

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Abstract

We show that the degree $d$ Jouanolou foliation $\mathcal J_d$ on $\mathbb P^2$ is structurally stable for every $d \geq 2$. We prove the existence of a neighbourhood $\mathcal U_d$ of $\mathcal J_d$, such that every foliation $\mathcal F \in \mathcal U_d$ satisfies: the Fatou set is a connected disc bundle over a compact Riemann surface of genus $d(d+1)/2$, no leaf is dense in $\mathbb P^2$, and all but countably many regular leaves are biholomorphic to the unit disc. Finally, we prove transverse perfectness of the Julia set on the regular locus for $d \geq 2$.

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BibTeX RIS

Sahil Gehlawat. 2026-09-28. Structural stability of the Jouanolou foliations in every degree. https://arxiv.org/abs/2609.35597

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