Degree of the first integral of a pencil in \(\mathbb{P}^2\) defined by Lins Neto. (English) Zbl 1281.32028

Medina, Liliana Puchuri

Publ. Mat., Barc. 57, No. 1, 123-137 (2013).

Summary: Let \(\mathcal{P}_4\) be the linear family of foliations of degree \(4\) in \(\mathbb{P}^2\) introduced by A. Lins Neto, whose set of parameters with first integral \(I_p(\mathcal{P}_4)\) is dense and countable. In this work, we compute explicitly the degree of the rational first integral of the foliations in this linear family, as a function of the parameter.

MSC:

32S65	Singularities of holomorphic vector fields and foliations
37F75	Dynamical aspects of holomorphic foliations and vector fields

Keywords:

Poincaré problem; pencil of foliations; first integral

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