Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completely reducible hypersurfaces in a pencil   We study completely reducible fibers of pencils of hypersurfaces on $\mathbb
P^n$ and associated codimension one foliations of $\mathbb P^n$.
  Using methods from theory of foliations we obtain certain upper bounds for
the number of these fibers as functions only of $n$.
  Equivalently this gives upper bounds for the dimensions of resonance
varieties of hyperplane arrangements.
  We obtain similar bounds for the dimensions of the characteristic varieties
of the arrangement complements.

36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph