Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Holomorphic vector fields tangent to foliations in dimension three   This article studies germs of holomorphic vector fields at the origin of C3
that are tangent to holomorphic foliations of codimension one. Two situations
are considered. First, we assume hypotheses on the reduction of singularities
of the vector field - for instance, that the final models belong to a family of
vector fields whose linear parts have eigenvalues satisfying a condition of
non-resonance - in order to conclude that the foliation is of complex
hyperbolic type, that is, without saddle-nodes in its reduction of
singularities. In the second part, we prove that a vector field that is tangent
to three independent foliations is tangent to a whole pencil of foliations -
hence, to infinitely many foliations - and, as a consequence, it leaves
invariant a germ of analytic surface. This final part is based on a local
version of a well-known characterization of pencils of foliations of
codimension one in projective spaces.

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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an