论文标题
在残留有限的Dedekind域上的超平面布置的特征性准分子分解
The Characteristic Quasi-Polynomials of Hyperplane Arrangements over Residually Finite Dedekind Domains
论文作者
论文摘要
Kamiya，Takemura和Terao启动了整体排列的特征准多项式的理论，这是一个函数，它计算了互补的元素模型阳性整数。 他们给出了一个特征性的准多项式时期，称为LCM - period，并表明特征性准多项式的第一个组成部分与相应超平面布置的特征多项式一致。 最近，刘，特兰（Liu）和吉（Yoshinaga）表明，特征性准多单位的最后一个成分与相应的复曲面排列的特征多项式相吻合。 另外，通过使用曲曲面理论，Higashitani，Tran和Yoshinaga证明了LCM-Period是特征性准多项式的最低时期。 在本文中，我们研究了对Dedekind域上的安排，使每个具有非零理想的残基环为有限，并给出上述结果的代数概括。
Kamiya, Takemura, and Terao initiated the theory of the characteristic quasi-polynomial of an integral arrangement, which is a function counting the elements in the complement of the arrangement modulo positive integers. They gave a period of the characteristic quasi-polynomial, called the LCM-period, and showed that the first constituent of the characteristic quasi-polynomial coincides with the characteristic polynomial of the corresponding hyperplane arrangement. Recently, Liu, Tran, and Yoshinaga showed that the last constituent of the characteristic quasi-polynomial coincides with the characteristic polynomial of the corresponding toric arrangement. In addition, by using the theory of toric arrangements, Higashitani, Tran, and Yoshinaga proved that the LCM-period is the minimum period of the characteristic quasi-polynomial. In this paper, we study an arrangements over a Dedekind domain such that every residue ring with a nonzero ideal is finite and give algebraic generalizations of the above results.
