Related papers: Deformation of Residual Intersections

If $I$ is a perfect ideal in a local Cohen-Macaulay ring, the generators of ideals linked to $I$ are well understood. However, the generators of the residual intersections of $I$ have only been computed in a few special cases. In this…

If I is an ideal in a Gorenstein ring S and S/I is Cohen-Macaulay, then the same is true for any linked ideal I'. However, such statements hold for residual intersections of higher codimension only under very restrictive hypotheses, not…

In this article we study the structure of residual intersections via constructing a finite complex which is acyclic under some sliding depth conditions on the cycles of the Koszul complex. This complex provides information on an ideal which…

An ideal I of a local Cohen-Macaulay ring R is called a cohomologically complete intersection if H^i_I(R) = 0 for all i \neq c = height(I). Here H^i_I(R), i \in Z denotes the local cohomology of R with respect to I. For instance, a…

D. Rees and J. Sally defined the core of an $R$-ideal $I$ as the intersection of all $($minimal$)$ reductions of $I$. However, it is not easy to give an explicit characterization of it in terms of data attached to the ideal. Until recently,…

While every grade 2 perfect ideal in a regular local ring is linked to a complete intersection ideal, it is known not to be the case for ideals of grade 3. We soften the blow by proving that every grade 3 perfect ideal in a regular local…

Inspired by the works in linkage theory of ideals, we define the concept of linkage of ideals over a module. Several known theorems in linkage theory are improved or recovered by new approaches. Specially, we make some extensions and…

In the present paper we investigate a question stemming from a long-standing conjecture of Vasconcelos: given a generically a complete intersection perfect ideal I in a regular local ring R, is it true that if I/I^2 (or R/I^2) is…

Given a simplicial complex, it is easy to construct a generic deformation of its Stanley-Reisner ideal. The main question under investigation in this paper is how to characterize the simplicial complexes such that their Stanley-Reisner…

Schemes defined by residual intersections have been extensively studied in the case when they are Cohen-Macaulay, but this is a very restrictive condition. In this paper we make the first study of a class of natural examples far from…

In this paper, we consider a finite, torsion-free module $E$ over a Gorenstein local ring. We provide sufficient conditions for $E$ to be of linear type and for the Rees algebra $\mathcal{R}(E)$ of $E$ to be Cohen-Macaulay. Our results are…

One describes generators of disguised residual intersections in any commutative Noetherian rings. It is shown that, over Cohen-Macaulay rings, the disguised residual intersections and algebraic residual intersections are the same, for…

We show that if $(R, \m)$ is a Cohen-Macaulay local ring and $I$ is an ideal of minimal mixed multiplicity, then $\depth G(I) \geq d- 1$ implies that $\depth F(I) \geq d-1$. We use this to show that if $I$ is a contracted ideal in a two…

We classify all binomial edge ideals that are complete intersection and Cohen-Macaulay almost complete intersection. We also describe an algorithm and provide an implementation to compute primary decomposition of binomial edge ideals.

This paper studies algebraic residual intersections in rings with Serre's condition \( S_{s} \). It demonstrates that residual intersections admit free approaches i.e. perfect subideal with the same radical. This fact leads to determining a…

Let $(A,\mathfrak{m})$ be a Cohen-Macaulay local ring of dimension $d \geq 2$ with infinite residue field and let $I$ be an $\mathfrak{m}$-primary ideal. For $0 \leq i \leq d$ let $I_i$ be the $i^{th}$-coefficient ideal of $I$. Also let…

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…

We show the Cohen-Macaulayness and describe the canonical module of residual intersections $J=\mathfrak{a}\colon_R I$ in a Cohen-Macaulay local ring $R$, under sliding depth type hypotheses. For this purpose, we construct and study, using a…

A quasi-complete intersection (q.c.i.) ideal of a local ring is an ideal with "free exterior Koszul homology"; the definition can also be understood in terms of vanishing of Andr\'e-Quillen homology functors. Principal q.c.i. ideals are…

Let $k$ be a field. We determine the ideals $I$ in a finitely generated graded $k$-algebra $A$, whose associated graded rings are isomorphic to $A$. Also we compute the graded local cohomologies of the Rees rings $A[I t]$ and give the…