Bernstein理想的超平面中央一般安排
Idéal de Bernstein d'un arrangement central générique d'hyperplans
摘要：
设$ V $是维数为$n$的向量空间.两两不同的矢量超平面的$V$族$ \{H_1, \ldots, H_p \} $定义了$ V $的排列$ {\cal A}_p = {\cal A} ( H_1, \ldots ,H_p ) $。对于$ i \in \{ 1, \ldots, p \} $，设$ l_i $是以$H_i$为核的$V$上的线性形式。如果布置的$n$超平面的每个子族的交集被减少到零，则这种布置是通用的。设$A_V ({\bf C}) $是代数微分算子的Weyl代数，其系数在$V$的对偶的对称代数$S$中。继伯恩斯坦，理想构成多项式$ b \in {\bf C} [s_1, \ldots, s_p] $，使：$$ \; \; b (s_1, \ldots, s_p) \, l_1^{s_1} \ldots l_p^{s_p} \in A_V ({\bf C}) [s_1, \ldots, s_p] \, l_1^ {s_1 + 1} \ldots l_p^{s_p + 1} $$不减少到零。这个理想不依赖于定义超曲面$H_i$的线性形式$l_i $的选择。这篇文章的目的就是为了实现这一理想。
英文摘要：
Let $ V $ a vector space of dimension $n$. A $V$ family $ \{H_1, \ldots, H_p \} $ of vectorial hyperplanes being distinct two by two defines an arrangement $ {\cal A}_p = {\cal A} ( H_1, \ldots ,H_p ) $ of $ V $. For $ i \in \{ 1, \ldots, p \} $, let $ l_i $ be a linear form on $V$ with $H_i$ as kernel. This arrangement is generic if the intersection of every sub-family of $n$ hyperplanes of the arranfement is reduced to zero. Let $A_V ({\bf C}) $, be the Weyl algebra of algebraic differential operators with coefficients in the symetric algebra denoted $S$ of the dual of $V$. Following J. Bernstein, the ideal constituted by polynomials $ b \in {\bf C} [s_1, \ldots, s_p] $ such that : $$ \; \; b (s_1, \ldots, s_p) \, l_1^{s_1} \ldots l_p^{s_p} \in A_V ({\bf C}) [s_1, \ldots, s_p] \, l_1^ {s_1 + 1} \ldots l_p^{s_p + 1} $$ is not reduced to zero. This ideal does not depend on the choice of linear forms $l_i $ which define the hypersurfaces $H_i$. The goal of this article is to precise this ideal.
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