论文标题
Artin单一理想的极化
Polarizations of Artin monomial ideals
论文作者
论文摘要
我们表明，任何对Artin单一理想的极化都定义了三角球。这证明了A.Almousa，H.Lohne和第一作者的猜想。 从几何上，包含$（x_1^{a_1}，\ ldots，x_n^{a_n}）$的理想的极化定义了球体上的全维三角球，这是维度简单的界限$ a_1-1，\ cdots，\ cdots，a_n-1 $。这种连接的球体的每个全维Cohen-Macaulay子复合物都是这样的，这些球都是可构造的。 这样的三角球具有一个双电池复合物，它是尺寸简单产品$ a_1-1，\ cdots a_n-1 $的子复合物的子复合物。相关的细胞络合物使三角球的亚历山大双重理想的自由分辨率最少。当简单的乘积是超越立方体时，在许多示例中，这些双重细胞复合物可以将Artin单一理想的极化范围分类。 我们还表明，G.Kalai \ cite {ka}的挤压球源自Artin单一理想的极化。
We show that any polarization of an Artin monomial ideal defines a triangulated ball. This proves a conjecture of A.Almousa, H.Lohne and the first author. Geometrically, polarizations of ideals containing $(x_1^{a_1}, \ldots, x_n^{a_n})$ define full-dimensional triangulated balls on the sphere which is the join of boundaries of simplices of dimensions $a_1-1, \cdots, a_n-1$. Every full-dimensional Cohen-Macaulay sub-complex of this joined sphere is of this kind, and these balls are constructible. Such a triangulated ball has a dual cell complex which is a sub-complex of the product of simplices of dimensions $a_1-1, \cdots a_n-1$. The associated cellular complex of this gives the minimal free resolution of the Alexander dual ideal of the triangulated ball. When the product of simplices is a hypercube, in many examples these dual cell complexes enables a classification of the range of polarizations of the Artin monomial ideal. We also show that the squeezed balls of G.Kalai \cite{Ka} derive from polarizations of Artin monomial ideals.
