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arXiv · 2608.06588

Projective Foliations with a Unique Singular Point and Maximum Algebraic Multiplicity

Jorge Mozo-Fernández·P. Rubí Pantaleón-Mondragón
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Abstract

The study of codimension-one holomorphic foliations on the projective plane $\mathbb{CP}^{2}$ with a unique singular point has attracted increasing interest because of its connections with several important problems. In this paper, we focus on holomorphic foliations of degree $d$ having a singular point of maximal multiplicity $d$. We describe explicitly the foliations in this class and characterize those having a unique singular point. We also state some results concerning Hilbert-Mumford stability for these foliations.

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Jorge Mozo-Fernández, P. Rubí Pantaleón-Mondragón. 2026-08-06. Projective Foliations with a Unique Singular Point and Maximum Algebraic Multiplicity. https://arxiv.org/abs/2608.06588

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