相关论文: Cohen-Macaulay fiber cones

Let $G$ be a simple graph on $n$ vertices and let $J_{G,m}$ be the generalized binomial edge ideal associated to $G$ in the polynomial ring $K[x_{ij}, 1\le i \le m, 1\le j \le n]$. We classify the Cohen-Macaulay generalized binomial edge…

We give bounds for the Hilbert-Kunz multiplicity of the product of two ideals, and we characterize the equality in terms of the tight closures of the ideals. Connections are drawn with $*$-spread and with ordinary length calculations.

Let $K$ be an infinite field and let $m_1,\ldots,m_n$ be a generalized arithmetic sequence of positive integers, i.e., there exist $h, d, m_1 \in\mathbb{Z}^+$ such that $m_i = h m_1 + (i-1)d$ for all $i \in \{2,\ldots,n\}$. We consider the…

The aim of this paper is to define the notion of the Cohen-Macaulay cone of a Noetherian local domain R and to present its application to the theory of Hilbert-Kunz functions. It has been shown in Kurano's paper "Numerical equivalence…

It is shown that the Orlik-Terao algebra is graded isomorphic to the special fiber of the ideal $I$ generated by the $(n-1)$-fold products of the members of a central arrangement of size $n$. This momentum is carried over to the Rees…

Foa a given local ring, we study the fiber cone of ideals with analytic spread one. In this case, the fiber cone has a strucure as a module over its Noether normalization which is a polynomial ring in one variable over the residue field.…

We characterize when the monomial maximal ideal of a simplicial affine semigroup ring has a monomial minimal reduction. When this is the case, we study the Cohen-Macaulay and Gorenstein properties of the associated graded ring and provide…

Let $R$ be a standard graded polynomial ring over a field $k$. The paper focuses on homogeneous ideals $J \subset R$ of codimension $2$ generated by three forms of the same degree $d \geq 2$ that are almost Cohen--Macaulay, i.e., of…

We study a large family of products of Borel fixed ideals of maximal minors. We compute their initial ideals and primary decompositions, and show that they have linear free resolutions. The main tools are an extension of straightening law…

In this paper, we study rooted products of graphs from the perspective of combinatorial commutative algebra. For edge ideals, we introduce the 2-Cohen-Macaulayness with respect to a vertex and use it to investigate when edge ideals of…

It is shown that a module is sequentially Cohen-Macaulay if and only if the index of reducibility for distinguished parameter ideals are eventually constant with special value. As corollaries to the main theorem we given to characterize the…

Let $(R,\frak{m})$ be a $d$-dimensional Cohen-Macaulay local ring, $I$ an $\frak{m}$-primary ideal and $J$ a minimal reduction of $I$. In this paper we study the independence of reduction ideals and the behavior of the higher Hilbert…

In this paper, we introduce initially Cohen-Macaulay modules over a commutative Noetherian local ring $R$, a new class of $R$-modules that generalizes both Cohen-Macaulay and sequentially Cohen-Macaulay modules. A finitely generated…

In this paper we study simplicial complexes as higher dimensional graphs in order to produce algebraic statements about their facet ideals. We introduce a large class of square-free monomial ideals with Cohen-Macaulay quotients, and a…

We construct a generalize Ishida complex to compute the local cohomology with monomial support of modules over quotients of polynomial rings by cellular binomial ideals. As a consequence, we obtain a combinatorial criterion to determine…

We investigate Borel ideals on the Hilbert scheme components of arithmetically Cohen-Macaulay (ACM) codimension two schemes in P^n. We give a basic necessary criterion for a Borel ideal to be on such a component. Then considering ACM curves…

This paper uses dualities between facet ideal theory and Stanley-Reisner theory to show that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay. The proof involves showing that the Alexander dual (or the cover dual, as we…

We present criteria for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of graph theory and of linear programming to study the Cohen-Macaulayness of monomial ideals…

We study weighted graphs and their "edge ideals" which are ideals in polynomial rings that are defined in terms of the graphs. We provide combinatorial descriptions of m-irreducible decompositions for the edge ideal of a weighted graph in…

Let $I$ be a homogeneous ideal in the polynomial ring $R = k[z_1, \cdots, z_n]$ , where $k$ is an algebraically closed field of characteristic zero. Macaulay's Theorem provides constraints on the Hilbert function of $I$ or $R/I$ from one…