Related papers: Minimal free resolution of monoimal ideals by iter…

This paper studies the algebraic structure of a new class of hyperplane arrangement $A$ obtained by deleting two hyperplanes from a free arrangement. We provide information on the minimal free resolutions of the logarithmic derivation…

We define the reduced horseshoe resolution and the notion of conjoined pairs of ideals in order to study the minimal graded free resolution of a class of p-Borel ideals and recover Pardue's regularity formula for them. It will follow from…

Let $R=\mathbb{K}[x_1,\dots,x_n]$, a graded algebra $S=R/I$ satisfies $N_{k,p}$ if $I$ is generated in degree $k$, and the graded minimal resolution is linear the first $p$ steps, and the $k$-index of $S$ is the largest $p$ such that $S$…

We study minimal reductions of edge ideals of graphs and determine restrictions on the coefficients of the generators of these minimal reductions. We prove that when $I$ is not basic, then $\core{I}\subset \m I$, where $I$ is an edge ideal…

We introduce the notion of Betti category for graded modules over suitably graded polynomial rings, and more generally for modules over certain small categories. Our categorical approach allows us to treat simultaneously many important…

Over an infinite field $K$, we investigate the minimal free resolution of some configurations of lines. We explicitly describe the minimal free resolution of "complete grids of lines" and obtain an analogous result about the so-called…

We consider powers of lexsegment ideals with a linear resolution (equivalently, with linear quotients) which are not completely lexsegment ideals. We give a complete description of their minimal graded free resolution.

In this paper, we study a class of toric ideals obtained by using some geometric data of ADE trees which are the minimal resolution graphs of rational surface singularities. We compute explicit Gr\"obner bases for these toric ideals that…

Consider an ideal $I\subset K[x_1,..., x_n]$, with $K$ an arbitrary field, generated by monomials of degree two. Assuming that $I$ does not have a linear resolution, we determine the step $s$ of the minimal graded free resolution of $I$…

For a finite simple graph $G$ and an integer $r \ge 1$, the $r$-connected ideal $I_r(G)$ is the squarefree monomial ideal generated by the vertex sets of connected induced subgraphs of size $r+1$, extending the classical edge ideal. We…

Using linear algebra methods we study certain algebraic properties of monomial rings and matroids. Let I be a monomial ideal in a polynomial ring over an arbitrary field. If the Rees cone of I is quasi-ideal, we express the normalization of…

We construct the first linear strand of the minimal free resolutions of edge ideals of $d$-partite $d$-uniform clutters. We show that the first linear strand is supported on a relative simplicial complex. In the case that the edge ideals of…

Each partition $\lambda = (\lambda_1, \lambda_2, ..., \lambda_n)$ determines a so-called Ferrers tableau or, equivalently, a Ferrers bipartite graph. Its edge ideal, dubbed Ferrers ideal, is a squarefree monomial ideal that is generated by…

Consider the affine space consisting of pairs of matrices $(A,B)$ of fixed size, and its closed subvariety given by the rank conditions $\operatorname{rank} A \leq a$, $\operatorname{rank} B \leq b$ and $\operatorname{rank} (A\cdot B) \leq…

We define and study Hodge ideals associated to a coherent ideal sheaf J on a smooth complex variety, via algebraic constructions based on the already existing concept of Hodge ideals associated to Q-divisors. We also define the generic…

We compute a minimal bigraded resolution of the Rees Algebra associated to a proper rational parametrization of a monomial plane curve. We describe explicitly both the bigraded Betti numbers and the maps of the resolution in terms of a…

In this paper, we introduce and study families of squarefree monomial ideals called clique ideals and independence ideals that can be associated to a finite graph. A family of clique ideals with linear resolutions has been characterized.…

For each squarefree monomial ideal $I\subset S = k[x_{1},\ldots, x_{n}] $, we associate a simple graph $G_I$ by using the first linear syzygies of $I$. In cases, where $G_I$ is a cycle or a tree, we show the following are equivalent: (a) $…

For a monomial ideal $I$, let $G(I)$ be its minimal set of monomial generators. If there is a total order on $G(I)$ such that the corresponding Lyubeznik resolution of $I$ is a minimal free resolution of $I$, then $I$ is called a Lyubeznik…

We investigate monomial labellings on cell complexes, giving a minimal cellular resolution of the ideal generated by these monomials, and such that the associated quotient ring is Cohen-Macaulay. We introduce a notion of such a labelling…