论文标题
弱封闭图的二项式边缘理想
Binomial edge ideals of weakly closed graphs
论文作者
论文摘要
Herzog等人的特征是封闭图。作为二项式边缘理想的图形，相对于对角线序列具有二次gröbner基础。在本文中，我们专注于封闭图的概括，即弱关闭的图（或共弥补的图形）。基于关于纳特森通用矩阵理想的一些结果，我们将弱封闭的图表描述为唯一的图形，其二项式边缘理想是Knutson的理想，用于某些多项式$ f $。在此过程中，我们重新启动了Matsuda的定理，以呈正性特征弱闭合图的二项式边缘理想的F纯度，并将其扩展到广义二项式边缘理想。此外，我们从其二项式边缘理想的最低限度来看，给出了弱闭合图的特征，我们为这种选择的$ f $选择了Knutson理想的所有最低素数。
Closed graphs have been characterized by Herzog et al. as the graphs whose binomial edge ideals have a quadratic Gröbner basis with respect to a diagonal term order. In this paper, we focus on a generalization of closed graphs, namely weakly-closed graphs (or co-comparability graphs). Build on some results about Knutson ideals of generic matrices, we characterize weakly closed graphs as the only graphs whose binomial edge ideals are Knutson ideals for a certain polynomial $f$. In doing so, we re-prove Matsuda's theorem about the F-purity of binomial edge ideals of weakly closed graphs in positive characteristic and we extend it to generalized binomial edge ideals. Furthermore, we give a characterization of weakly closed graphs in terms of the minimal primes of their binomial edge ideals and we characterize all minimal primes of Knutson ideals for this choice of $f$.
