Degree of the First Integral of a Foliation in the Pencil $\mathcal{P}_4$

Details Degree of the First Integral of a Foliation in the Pencil $\mathcal{P}_4$ Degree of the First Integral of a Foliation in the Pencil $\mathcal{P}_4$

2011-04-30

arxiv.org/abs/1105.0104v1

Mathematics

Complex Variables

Scientific paper

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

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