论文标题
亚辅助性，链连通性和多式贝蒂数字的单一理想数量
Subadditivity, strand connectivity and multigraded Betti numbers of monomial ideals
论文作者
论文摘要
令$ r = \ mathbb {k} [x_1，\ ldots，x_n] $和$ i \ subset r $是同质的理想。在本文中，我们首先获得了$ r/i $的子贴的某些足够条件。结果，我们证明，如果$ i $是由均质完整的交叉点产生的，那么子效率为$ r/i $。然后，当$ i $是$ r/i $ koszul的单一理想时，我们就将Avramov，Conca和Iyengar的猜想进行了研究。我们确定了几类的图形理想$ g $，以使该子粘性以$ r/i（g）$的含量为单位。然后，我们研究边缘理想的链连接性，并获得几类的图形，这些图形与边缘理想相连。最后，我们计算了几类边缘理想的多式贝蒂数字的上限。
Let $R = \mathbb{K}[x_1, \ldots, x_n]$ and $I \subset R$ be a homogeneous ideal. In this article, we first obtain certain sufficient conditions for the subadditivity of $R/I$. As a consequence, we prove that if $I$ is generated by homogeneous complete intersection, then subadditivity holds for $R/I$. We then study a conjecture of Avramov, Conca and Iyengar on subadditivity, when $I$ is a monomial ideal with $R/I$ Koszul. We identify several classes of edge ideals of graphs $G$ such that the subadditivity holds for $R/I(G)$. We then study the strand connectivity of edge ideals and obtain several classes of graphs whose edge ideals are strand connected. Finally, we compute upper bounds for multigraded Betti numbers of several classes of edge ideals.
