Related papers: Normal Rees algebras arising from vertex decomposa…

We establish a genericity property in the representation theory of a flat family of finite-dimensional algebras in the sense of Cline-Parshal-Scott. More precisely, we show that the decomposition matrices as introduced by Geck and Rouquier…

Let $S=K[x_1,\dots,x_n]$ be the polynomial ring over a field $K$ and $I\subset S$ be a squarefree monomial ideal generated in degree $n-2$. Motivated by the remarkable behavior of the powers of $I$ when $I$ admits a linear resolution, as…

We investigate the Gauss algebra for squarefree Veronese algebras generated in degree $3$. For small dimensions not exceeding $7$, we determine the Gauss algebra by specifying its generators and show in particular that it is normal and…

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.…

Our main theorems provide a single geometric setting in which polynomial representatives for Schubert classes in the integral cohomology ring of the flag manifold are determined uniquely, and have positive coefficients for geometric…

We study almost complete intersections ideals whose Rees algebras are extremal in the sense that some of their fundamental metrics---depth or relation type---have maximal or minimal values in the class. The focus is on those ideals that…

Let $S=K[x_1,\dots,x_n]$ be the polynomial ring over a field $K$, and let $I\subset S$ be a monomial ideal. In this paper, we introduce the $i$th \textit{homological shift algebras}…

The cut sets of a graph are special sets of vertices whose removal disconnects the graph. They are fundamental in the study of binomial edge ideals, since they encode their minimal primary decomposition. We introduce the class of accessible…

In this paper, we introduce techniques for producing normal square-free monomial ideals from old such ideals. These techniques are then used to investigate the normality of cover ideals under some graph operations. Square-free monomial…

Ehrenborg, Govindaiah, Park, and Readdy recently introduced the van der Waerden complex, a pure simplicial complex whose facets correspond to arithmetic progressions. Using techniques from combinatorial commutative algebra, we classify when…

We study the minimal primary decomposition of completely $t$-spread lexsegment ideals via simplicial complexes. We determine some algebraic invariants of such a class of $t$-spread ideals. Hence, we classify all $t$-spread lexsegment ideals…

The study of the edge ideal $I(D_{G})$ of a weighted oriented graph $D_{G}$ with underlying graph $G$ started in the context of Reed-Muller type codes. We generalize a Cohen-Macaulay construction for $I(D_{G})$, which Villarreal gave for…

Let $I \subset R = \mathbb{F}[x_1,x_2]$ be a height two ideal minimally generated by three homogeneous polynomials of the same degree $d$, where $\mathbb{F}$ is a field of characteristic zero. We use the theory of $D$-modules to deduce…

Consider a height two ideal, $I$, which is minimally generated by $m$ homogeneous forms of degree $d$ in the polynomial ring $R=k[x,y]$. Suppose that one column in the homogeneous presenting matrix $\f$ of $I$ has entries of degree $n$ and…

Let $X$ be the Hankel matrix of size $2\times n$ and let $G$ be a closed graph on the vertex set $[n].$ We study the binomial ideal $I_G\subset K[x_1,\ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which correspond to the…

In this paper, we obtain a generalization, in dimension $3$, of a theorem of David Rees about joint reductions of the bigraded filtration $\{ \overline{I^rJ^s}\}$ of complete ${\mathfrak m}$-primary ideals and vanishing of the second normal…

Let $(A,\mathfrak{m})$ be an excellent normal domain of dimension two. We define an $\mathfrak{m}$-primary ideal $I$ to be a $p_g$-ideal if the Rees algebra $A[It]$ is a Cohen-Macaulay normal domain. When $A$ contains an algebraically…

We study the symbolic powers of square-free monomial ideals via symbolic Rees algebras and methods in prime characteristic. In particular, we prove that the symbolic Rees algebra and the symbolic associated graded algebra are split with…

In this paper we discuss the problem of characterizing the Cohen-Macaulay property of certain families of monomial ideals with fixed radical. More precisely, we consider generically complete intersection monomial ideals whose radical…

In this paper we consider multi-graded extended Rees algebras of zero dimensional ideals which are Cohen-Macaulay (CM) with minimal multiplicity. We show that the minimal multiplicity property can occur only for the ordinary extended Rees…