论文标题
外边缘理想的深度和奇异品种
Depth and Singular Varieties of Exterior Edge Ideals
论文作者
论文摘要
有限简单图的边缘理想在多项式环上进行了充分研究。在本文中，我们启动了对外部代数的边缘理想的研究，专门针对此类理想的深度和奇异品种。我们证明了与一般图相关的边缘深度的上限，并且在两部分图中具有更精致的绑定，我们证明两者都很紧。我们还计算了几个大型图的深度，包括循环，完整的多部分图，蜘蛛图和弗雷尔图。最后，我们专注于图形对相关边缘理想深度的效果。
Edge ideals of finite simple graphs are well-studied over polynomial rings. In this paper, we initiate the study of edge ideals over exterior algebras, specifically focusing on the depth and singular varieties of such ideals. We prove an upper bound on the depth of the edge ideal associated to a general graph and a more refined bound for bipartite graphs, and we show that both are tight. We also compute the depth of several large families of graphs including cycles, complete multipartite graphs, spider graphs, and Ferrers graphs. Finally, we focus on the effect whiskering a graph has on the depth of the associated edge ideal.
