相关论文: Edge ideals and their asymptotic syzygies

In this paper we examine the commutativity of ideal extensions. We introduce methods of constructing such extensions, in particular we construct a noncommutative ring T which contains a central and idempotent ideal I such that T/I is a…

Symmetric strongly shifted ideals are a class of monomial ideals which come equipped with an action of the symmetric group and are analogous to the well-studied class of strongly stable monomial ideals. In this paper we focus on algebraic…

The main aim of this paper is to bridge two directions of research generalizing asymptotic density zero sets. This enables to transfer results concerning one direction to the other one. Consider a function $g\colon\omega\to [0,\infty)$ such…

Topological materials exhibit edge-localized scattering-free modes protected by their nontrivial bulk topology through the bulk-edge correspondence in Hermitian systems. While topological phenomena have recently been much investigated in…

In this paper, we investigate the degree of $h$-polynomials of edge ideals of finite simple graphs. In particular, we provide combinatorial formulas for the degree of the $h$-polynomial for various fundamental classes of graphs such as…

This work concerns the linearity defect of a module $M$ over a noetherian local ring $R$, introduced by Herzog and Iyengar in 2005, and denoted by $\text{ld}_R M$. Roughly speaking, $\text{ld}_R M$ is the homological degree beyond which the…

In this paper, we study associated primes and depth of integral closures of powers of edge ideals. We provide sharp bounds on how big of powers for which the set of associated primes and the depth of integral closures of powers of edge…

Let $\mathscr{I}$ be an ideal sheaf on $P^n$. In the first part of this paper, we bound the asymptotic regularity of powers of $\mathscr{I}$ as $ps-3\leq \reg \mathscr{I}^p\leq ps+e$, where $e$ is a constant and $s$ is the $s$-invariant of…

In this paper we prove that if $I(G)$ is a bipartite edge ideal with regularity three then for all $s\geq 2$ the regularity of $I(G)^s$ is exactly $2s+1$.

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal in a polynomial ring over a field $\mathbb{K}$. In this paper, we obtain upper bounds for the Castelnuovo-Mumford regularity of symbolic powers of certain…

Let $R$ be a standard graded algebra over a field $k$, with irrelevant maximal ideal $\fm$, and $I$ a homogeneous $R$-ideal. We study the asymptotic vanishing behavior of the graded components of the local cohomology modules…

Let $C$ be a commutative Noetherian ring containing a field $K$ of characteristic zero. Let $R=C[X_1, \ldots, X_n, Y_1, \ldots, Y_m]$ be a polynomial ring over $C$ with $\mathrm{bideg}~ c=(0,0)$ for all $c \in C$, $\mathrm{bideg}~…

Let $A$ be a semigroup whose only invertible element is 0. For an $A$-homogeneous ideal we discuss the notions of simple $i$-syzygies and simple minimal free resolutions of $R/I$. When $I$ is a lattice ideal, the simple 0-syzygies of $R/I$…

A fruitful contemporary paradigm in graph theory is that almost all graphs that do not contain a certain subgraph have common structural characteristics. The "almost" is crucial, without it there is no structure. In this paper we transfer…

We prove the multiplicity bounds conjectured by Herzog-Huneke-Srinivasan and Herzog-Srinivasan in the following cases: the strong conjecture for edge ideals of bipartite graphs, and the weaker Taylor bound conjecture for all quadratic…

The geometric vertex decomposability property for polynomial ideals is an ideal-theoretic generalization of the vertex decomposability property for simplicial complexes. Indeed, a homogeneous geometrically vertex decomposable ideal is…

We study the regularity of symbolic powers of square-free monomial ideals. We prove that if $I = I_\Delta$ is the Stanley-Reisner ideal of a simplicial complex $\Delta$, then $\reg(I^{(n)}) \leqslant \delta(n-1) +b$ for all $n\geqslant 1$,…

Let $G$ be a finitely generated abelian group, and let $S = A[x_1, ..., x_n]$ be a $G$-graded polynomial ring over a commutative ring $A$. Let $I_1, ..., I_s$ be $G$-homogeneous ideals in $S$, and let $M$ be a finitely generated $G$-graded…

Let $\mathscr{I}$ be an ideal sheaf on $P^n$ defining a subscheme $X$. Associated to $\mathscr{I}$ there are two elementary invariants: the invariant $s$ which measures the positivity of $\mathscr{I}$, and the minimal number $d$ such that…

We provide a characterisation of all graphs whose parity binomial edge ideals have pure resolutions. In particular, we show that the minimal free resolution of a parity binomial edge ideal is pure if and only if the corresponding graph is a…