Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher codimensional foliations and Kupka singularities   We consider holomorphic foliations of dimension $k>1$ and codimension $\geq
1$ in the projective space $\mathbb{P}^n$, with a compact connected component
of the Kupka set. We prove that, if the transversal type is linear with
positive integers eigenvalues, then the foliation consist on the fibers of a
rational fibration. As a corollary, if $\mathcal{F}$ is a foliation such that
$dim(\mathcal{F})\geq cod(\mathcal{F})+2$ and has transversal type diagonal
with different eigenvalues, then the Kupka component $K$ is a complete
intersection and we get the same conclusion. The same conclusion holds if the
Kupka set is a complete intersection and has radial transversal type. Finally,
as an application, we find a normal form for non integrable codimension one
distributions on $\mathbb{P}^{n}$.

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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an