Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L'id\'eal de Bernstein d'un arrangement libre d'hyperplans lin\'eaires   Let $ V $ a vector space of dimension $n$. A family $ \{H_1, \ldots, H_p \} $
of vectorial hyperplans $V$ defines an arrangement $ {\cal A} $ of $ V $. For $
i \in \{ 1, \ldots, p \} $, let $ l_i $ be a linear form on $V$ with $H_i$ as
kernel. We denote by $A_V ({\bf C}) $, the Weyl algebra of algebraic
differential operators on $V$. Following J. Bernstein, the ideal constituted by
polynomials $ b \in {\bf C} [s_1, \ldots, s_p] $ such that : $$ \; \; b (s_1,
\ldots, s_p) \, l_1^{s_1} \ldots l_p^{s_p} \in A_n ({\bf C}) [s_1, \ldots, s_p]
\, l_1^ {s_1 + 1} \ldots l_p^{s_p + 1} \; , $$ is not reduced to zero. This
ideal does not depend on the choice of linear forms $ l_i $. The goal of this
article is to determine this ideal when $ {\cal A} $ is a free arrangement
constituted by linear hyperplans within the meaning of K. Saito.

25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci