Related papers: Residual Intersections and Linear Powers

Inspired by the work of Ulrich and Huneke-Ulrich, we describe a pattern to show that the ideals of certain opposite embedded Schubert varieties defined by this pattern arise by taking residual intersections of two geometrically linked…

We investigate the higher divisorial ideal $D(I):= Ann(Ext^g_R(R/I,R))$ associated to an ideal I of grade g. Our main focus is the containment problem $D(I) \subseteq \overline{I}$. We show that this inclusion holds for broad classes of…

Let $R=k[x_{1},\ldots,x_{n}]$, where $k$ is a field. The path ideal (of length $t\geq 2$) of a directed graph $G$ is the monomial ideal, denoted by $I_{t}(G)$, whose generators correspond to the directed paths of length $t$ in $G$. Let…

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…

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…

In this paper, we prove that if $I\subset S:=K[x_1,...,x_n]$ is a monomial ideal then $I$ and $S/I$ satisfy the Stanley conjecture when $I$ has a small number of generators, with respect to $\depth(S/I)$ and $\max\{|P|:\;P\in\Ass(S/I)\}$.…

There is a well known link from the first topic in the title to the third one. In this paper we thread that link through the second topic. The central result is a criterion for the tensor nilpotence of morphisms of perfect complexes over…

In this article, we investigate the $\operatorname{v}$-numbers of powers of monomial ideals and their integral closures in a polynomial ring $S$. We provide an alternative proof for determining the $\operatorname{v}$-numbers of powers of…

Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all…

Let $(R,\fm)$ be a Cohen-Macaulay local ring. If $R$ has a canonical module, then there are some interesting results about duality for this situation. In this paper, we show that one can indeed obtain similar these results in the case $R$…

Let R = k[[x_0,...,x_d]]/(f), where k is a field and f is a non-zero non-unit of the formal power series ring k[[x_0,...,x_d]]. We investigate the question of which rings of this form have bounded Cohen--Macaulay type, that is, have a bound…

Conca and Varbaro (Invent. Math. 221 (2020), no. 3) showed the equality of depth of a graded ideal and its initial ideal in a polynomial ring when the initial ideal is square-free. In this paper, we give some beautiful applications of this…

Let $R$ be a Cohen-Macaulay local ring, $I$ a strongly Cohen-Macaulay ideal of $R$. We show that $R/{\rm Ann}_R(I)$ is a maximal Cohen-Macaulay $R$-module by means of the delta-invariant. Also it is shown that there exists a Cohen-Macaulay…

Let $I$ be the edge ideal of a Cohen-Macaulay tree of dimension $d$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_{d},y_1,\ldots,y_d]$. We prove that for all $t \ge 1$, $$\operatorname{depth} (S/I^t) = \operatorname{max} \{d -t + 1, 1…

The core of an ideal is defined as the intersection of all of its reductions. In this paper we provide an explicit description for the core of a monomial ideal $I$ satisfying certain residual conditions, showing that ${\rm core}(I)$…

One studies the structure of the Rees algebra of an almost complete intersection monomial ideal of finite co-length in a polynomial ring over a field, assuming that the least pure powers of the variables contained in the ideal have the same…

We study monomial ideals with linear presentation or partially linear resolution. We give combinatorial characterizations of linear presentation for square-free ideals of degree 3, and for primary ideals whose resolutions are linear except…

Inspired by the works in linkage theory of ideals, the concept of sliding depth of extension modules is defined to prove the Cohen-Macaulyness of linked module if the base ring is merely Cohen-Macaulay. Some relations between this new…

The subject matter is the structure of the Rees algebra of almost complete intersection ideals of finite colength in low-dimensional polynomial rings over fields. The main tool is a mix of Sylvester forms and iterative mapping cone…

In the first part of this paper we study scrollers and linearly joined varieties. A particular class of varieties, of important interest in classical Geometry are Cohen--Macaulay varieties of minimal degree. They appear naturally studying…