论文标题
小深度的二项式边缘理想
Binomial edge ideals of small depth
论文作者
论文摘要
令$ g $为$ [n] $和$ j_g $的图形为$ g $ $ g $在多项式环$ s = \ mathbb {k} [x_1，\ ldots，x_n，y_1，y_1，\ ldots，y__n] $中。在本文中，我们研究了与$ j_g $的最小主要分解相关的poset的一些拓扑特性。我们表明，该POSET承认了一些可签约的特定子搜索。反过来，这提供了一些有趣的代数后果。特别是，我们表征了所有图表$ g $，$ \ mathrm {depth} \ hspace {1.2mm} s/j_g = 4 $。
Let $G$ be a graph on $[n]$ and $J_G$ be the binomial edge ideal of $G$ in the polynomial ring $S=\mathbb{K}[x_1,\ldots,x_n,y_1,\ldots,y_n]$. In this paper we investigate some topological properties of a poset associated to the minimal primary decomposition of $J_G$. We show that this poset admits some specific subposets which are contractible. This in turn, provides some interesting algebraic consequences. In particular, we characterize all graphs $G$ for which $\mathrm{depth}\hspace{1.2mm} S/J_G=4$.
