Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Roots of the characteristic polynomials of hyperplane arrangements and
  their restrictions and localizations   Terao's factorization theorem shows that if an arrangement is free, then its
characteristic polynomial factors into the product of linear polynomials over
the integer ring. This is not a necessary condition, but there are not so many
non-free arrangements whose characteristic polynomial factors over the integer
ring. On the other hand, the localization of a free arrangement is free, and
its restriction is in many cases free, thus its characteristic polynomial
factors. In this paper, we consider how their integer, or real roots behave.

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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat