论文标题
在基本的双G-link上，无方形理想
On basic double G-links of squarefree monomial ideals
论文作者
论文摘要
Nagel和Römer引入了弱顶点分解的简单复合物，其中包括Matroid，Shifted和Gorenstein Complexs以及顶点可分解的复合物。他们证明了每个弱顶点可分解的简单复合物的史丹利 - 赖斯纳理想是戈伦斯坦通过一系列基本的双G-link序列与不确定的理想联系在一起的。在本文中，我们探讨了超出弱顶点分解设置之外的无方形单体理想之间的基本双重链接。 我们的第一个贡献是涉及边缘理想的某些基本双重链接的结构性结果。具体来说，假设$ i（g）$是图$ g $的边缘理想。当$ i（g）$是任意同质理想$ a $的单一理想$ b $的基本双g-link时，我们给出了$ g $的$ b $的生成集，并表明这种基本的双g-link必须为$ 1 $。我们的第二个重点是来自已知是Cohen-Macaulay的简单复合物的示例，但不能弱的顶点分解。我们表明，这些示例不是任何其他无方形单样理想的基本双链接。
Nagel and Römer introduced the class of weakly vertex decomposable simplicial complexes, which include matroid, shifted, and Gorenstein complexes as well as vertex decomposable complexes. They proved that the Stanley-Reisner ideal of every weakly vertex decomposable simplicial complex is Gorenstein linked to an ideal of indeterminates via a sequence of basic double G-links. In this paper, we explore basic double G-links between squarefree monomial ideals beyond the weakly vertex decomposable setting. Our first contribution is a structural result about certain basic double G-links which involve an edge ideal. Specifically, suppose $I(G)$ is the edge ideal of a graph $G$. When $I(G)$ is a basic double G-link of a monomial ideal $B$ on an arbitrary homogeneous ideal $A$, we give a generating set for $B$ in terms of $G$ and show that this basic double G-link must be of degree $1$. Our second focus is on examples from the literature of simplicial complexes known to be Cohen-Macaulay but not weakly vertex decomposable. We show that these examples are not basic double links of any other squarefree monomial ideals.
