论文标题
史丹利 - 赖斯纳折线环的线性分级线性折断电路络合物
Graded Linearity of Stanley-Reisner Ring of Broken Circuit Complexes
论文作者
论文摘要
本文介绍了两个新的级线性分辨率和渐变线性标准的新概念，这些概念概括了线性分辨率属性的概念和模块上多项式环$ a = k [x_1，\ dots，x_n] $上的模块的线性商概念。此外，我们将渐变线性与一般的线性线性进行比较。对于以$ a $的最大理想为基础的常规序列生成的模块，我们表明逐渐的线性商表示结肠理想的分级线性分辨率属性。另一方面，我们为破碎电路复合物的Stanley-Reisner环提供了分级线性分辨率特性的特定表征，并将\ cite {rv}的几个结果推广到矩形分解为均匀矩形的直接总和。具体而言，我们表明可以对矩阵进行分层，以使每个层都有分解为均匀的基质体。我们还为Orlik-Terao的超平面布置理想的结果提供了类似物，这是矩阵上相应结果的翻译。
This paper introduces two new notions of graded linear resolution and graded linear quotients, which generalize the concepts of linear resolution property and linear quotient for modules over the polynomial ring $A=k[x_1, \dots ,x_n]$. Besides, we compare graded linearity with componentwise linearity in general. For modules minimally generated by a regular sequence in a maximal ideal of $A$, we show that graded linear quotients imply graded linear resolution property for the colon ideals. On the other hand, we provide specific characterizations of graded linear resolution property for the Stanley-Reisner ring of broken circuit complexes and generalize several results of \cite{RV} on the decomposition of matroids into the direct sum of uniform matroids. Specifically, we show that the matroid can be stratified such that each strata has a decomposition into uniform matroids. We also present analogs of our results for the Orlik-Terao ideal of hyperplane arrangements which are translations of the corresponding results on matroids.
