Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On first order deformations of homogeneous foliations   We study analytic deformations of holomorphic foliations given by homogeneous
integrable one-forms in the complex affine space $\mathbb C^n$. The deformation
is supposed to be of first order (order one in the parameter). We also assume
that the deformation is given by homogeneous polynomial one-forms. The
deformation takes place in the affine space since we are not assuming that the
foliations descent to the projective space. We describe the space of such
deformations in three main situations: (1) the given foliation is given by the
level hypersurfaces of a homogeneous polynomial. (2) the foliation is rational,
ie., has a first integral of type $P^r/Q^s$ for some homogeneous polynomials
$P,Q$. (3) the foliation is logarithmic of a generic type.
  We prove that, for each class above, the first order homogeneous deformations
of same degree are in the very same class. We also investigate the existence of
such deformations with different degree.

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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex