Bernstein关于超平面线性自由排列的理想
L'idéal de Bernstein d'un arrangement libre d'hyperplans linéaires
摘要：
设$ V $是维数为$n$的向量空间。矢量超计划$V$族$ \{H_1, \ldots, H_p \} $定义了$ V $的布置$ {\cal A} $。对于$ i \in \{ 1, \ldots, p \} $，设$ l_i $是以$H_i$为核的$V$上的线性形式。我们用$A_V ({\bf C}) $表示$V$上的代数微分算子的Weyl代数。继伯恩斯坦，理想构成多项式$ b \in {\bf C} [s_1, \ldots, s_p] $，使：$$ \; \; b (s_1, \ldots, s_p) \, l_1^{s_1} \ldots l_p^{s_p} \in A_n ({\bf C}) [s_1, \ldots, s_p] \, l_1^ {s_1 + 1} \ldots l_p^{s_p + 1} \; , $$不减少到零。这种理想不依赖于线性形式$ l_i $的选择。本文的目标是确定当$ {\cal A} $是由K意义下的线性超平面构成的自由排列时的理想。齐藤
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
