Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degree of the First Integral of a Foliation in the Pencil
  $\mathcal{P}_4$   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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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph