Related papers: Waldschmidt constant of monomial ideals and Simis …

In this paper we investigate the class of rigid monomial ideals. We give a characterization of the minimal free resolutions of certain classes of these ideals. Specifically, we show that the ideals in a particular subclass of rigid monomial…

Let $I\subset S$ be a graded ideal of a standard graded polynomial ring $S$ with coefficients in a field $K$, and let $\text{v}(I)$ be the $\text{v}$-number of $I$. In previous work, we showed that for any graded ideal $I\subset S$…

It is shown that any set of nonzero monomial prime ideals can be realized as the stable set of associated prime ideals of a monomial ideal. Moreover, an algorithm is given to compute the stable set of associated prime ideals of a monomial…

Let $I$ be a squarefree monomial ideal of a polynomial algebra over a field minimally generated by $f_1,...,f_r$ of degree $ d\geq 1$, and a set $E$ of monomials of degree $\geq d+1$. Let $J\subsetneq I$ be a squarefree monomial ideal…

Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field. Suppose that $I$ is generated by one squarefree monomial of degree $ d>0$, and other squarefree monomials of degrees $\geq d+1$. If the Stanley…

Let $I\supsetneq J$ be two square free monomial ideals of a polynomial algebra over a field generated in degree $\geq 1$, resp. $\geq 2$ . Almost always when $I$ contains precisely one variable, the other generators having degrees $\geq 2$,…

Call a monomial ideal M "generic" if no variable appears with the same nonzero exponent in two distinct monomial generators. Using a convex polytope first studied by Scarf, we obtain a minimal free resolution of M. Any monomial ideal M can…

Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is either generated by three monomials of degrees $d$ and a set of monomials of…

Let $I$ be a monomial squarefree ideal of a polynomial ring $S$ over a field $K$ such that the sum of every three different of its minimal prime ideals is the maximal ideal of $S$, or more general a constant ideal. We associate to $I$ a…

In this paper, we focus on the associated primes of powers of monomial ideals and asymptotic behavior properties such as normally torsion-freeness, normality, the strong persistence property, and the persistence property. In particular, we…

Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is generated by three monomials of degrees $d$. If the Stanley depth of $I/J$ is…

Let $I$ be an ideal of a polynomial algebra $S$ over a field generated by square free monomials of degree $\geq d$. If $I$ contains more monomials of degree $d$ than $(n-d)/(n-d+1)$ of the total number of square free monomials of $S$ of…

Let $K$ be a infinite field, $S=K[x_1,\ldots,x_n]$ and $0\subset I\subsetneq J\subset S$ two squarefree monomial ideals. In a previous paper we proved a new formula for the Hilbert depth of $J/I$. In this paper, we illustrate how one can…

The aim of this work is to compare symbolic and ordinary powers of monomial ideals using commutative algebra and combinatorics. Monomial ideals whose symbolic and ordinary powers coincide are called Simis ideals. Weighted monomial ideals…

The aims of this work are to study Rees algebras of filtrations of monomial ideals associated to covering polyhedra of rational matrices with non-negative entries and non-zero columns using combinatorial optimization and integer…

In this paper, we first show that any square-free monomial ideal in $K[x_1, x_2, x_3, x_4, x_5]$ has the strong persistence property. Next we will provide a criterion for a minimal counterexample to the Conforti-Cornuejols conjecture.…

Continuing a well established tradition of associating convex bodies to monomial ideals, we initiate a program to construct asymptotic Newton polyhedra from decompositions of monomial ideals. This is achieved by forming a graded family of…

In [7] we obtained a formula for the Hilbert depth of squarefree Veronese ideals in a standard graded polynomial ring by relating it to the Hilbert depth of powers of the irrelevant maximal ideal. In this paper, we prove that these two…

Let $I\subset S=\KK[x_1,...,x_n]$ be a lexsegment ideal, generated by monomials of degree $d$. The main aim of this paper is to characterize when the Hilbert depth of $I$ will be 1, in the standard graded case. In addition to this, we will…

Irreducible decompositions of monomial ideals in polynomial rings over a field are well-understood. In this paper, we investigate decompositions in the set of monomial ideals in the semigroup ring A[\mathbb{R}_{\geq 0}^d] where A is an…