The Cohen-Macaulayness of the bounded complex of an affine oriented matroid
The Cohen-Macaulayness of the bounded complex of an affine oriented matroid
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DOI：
10.1016/j.jcta.2018.01.004
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发表时间：
2015-12
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影响因子：
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通讯作者：
R. Okazaki;Kohji Yanagawa
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文献类型：
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作者：
R. Okazaki;Kohji Yanagawa
仿射定向拟阵M是仿射超平面排列的组合抽象。Novik，Postnikov和Sturmfels [11]从M出发，构造了多项式环S_n中的一个无平方根的单项理想O_M，并得到了漂亮的结果.发展他们的理论，我们将展示以下内容。(1)若S_n/O_M是Cohen-Macaulay，则有界复形B_M（与M相伴的正则CW复形）是一个有边界的可收缩同调流形.这与Dong定理（[5]）密切相关，Dong定理曾是Zaslavsky猜想。(2)我们给出了M的一个刻划，使得S ∈ M/OM是Cohen-Macaulay，这说明[11，推论2.6]的匡威本质上是真的.
An affine oriented matroid M is a combinatorial abstraction of an affine hyperplane arrangement. From M, Novik, Postnikov and Sturmfels [11] constructed a squarefree monomial ideal O M in a polynomial ring S˜, and got beautiful results. Developing their theory, we will show the following.(1) If S˜/O M is Cohen–Macaulay, then the bounded complex B M (a regular CW complex associated with M) is a contractible homology manifold with boundary. This is closely related to Dong's theorem ([5]), which used to be Zaslavsky's conjecture.(2) We give a characterization of M such that S˜/O M is Cohen–Macaulay, which states that the converse of [11, Corollary 2.6] is essentially true.