超平面构形及其特征多项式

The Hyperplane Arrangements and Their Characteristic Polynomials

一个超平面构形是有限维向量空间中的有限个仿射超平面的集合。可以用数学领域很多学科的方法来研究超平面构形,例如:组合学、代数学、代数几何学、拓扑学、群作用等等,构形的研究结果将这些学科中看似毫无联系的知识联系在一起。不通过特征多项式的计算,求出了一些特殊构形的特征多项式中含有的因式,并利用图论中的顶点着色理论得到编织构形及某些子构形的特征多项式。

An arrangement of hyperplanes is a finite set of affine hyperplanes in a finite dimensional vector space. We study arrangements with methods from combinatorics, algebra, algebraic geometry, topolopy and group actions. Their study reveals unexpected connections of these areas. We give the factors for the characteristic polynomials of some spe-cial arrangements by not calculating their characteristic polynomials,and obtain the characteristic polynomials of braid ar-rangement and its subarrangements by coloring the vertices of their corresponding graphs.