arXiv subjects

Khadijeh Sayyari

Publications and source records attributed to Khadijeh Sayyari.

8 recordsLinked to original sources

arXiv2026

Linked sheaves of modules

We introduce a notion of linkage for sheaves of modules on connected Noetherian schemes, extending classical linkage of modules. Linkage is defined for stable sheaves admitting finite free resolutions via the transpose and syzygy functors. We show that linkedness is a local property and that, on affine schemes, a coherent sheaf is linked if and only if its module of global sections is linked. We further show that linkage is preserved under restriction and, under suitable rank conditions, under gluing over connected schemes. We also obtain criteria for the existence of linked subsheaves when the structure sheaf is not a domain. In the projective setting, we compare invariants of linked sheaves, including graded cohomology modules, Castelnuovo-Mumford regularity, and Hilbert polynomials.

math.AC↗

arXiv2025

Linkage of sheaves of modules

Inspired by the works in linkage theory of modules, we define the concept of linkage of sheaves of modules as a generalization of linkage of modules. Thus, we expressed it in geometry algebraic language. We show that the linkedness of sheaves is a locally property. As an important result, we have shown that the sheaf of modules made of Glueing schemes and Glueing linked sheaves of modules is a linked sheaf. Also, it has been shown that for every sheaf of modules on non-domain, it is possible to obtain a maximal linked subsheaf of modules.

math.AG↗

arXiv2021

Asymptotic behaviour of graded local cohomology modules via linkage

Assume that $R=\oplus_{n\in \mathbb{N}_0}R_n$ is a standard graded algebra over the local ring $(R_0,\mathfrak{m}_0)$, $\mathfrak{a}$ is a homogeneous ideal of $R$, $M$ is a finitely generated graded $R$-module and $R_+:=\oplus_{n\in \mathbb{N}}R_n$ denotes the irrelevant ideal of $R$. In this paper, we study the asymptotic behaviour of the set $\{ \operatorname{grade}(\mathfrak{a} \cap R_0, H^{\operatorname{grade}(R_+,M)}_{R_+}(M)_n) \}_{n \in \mathbb{Z}}$ as $n \rightarrow -\infty$, in the case where $\mathfrak{a}$ and $R_+$ are homogenously linked over $M$.

math.AC↗

arXiv2021

Graded local cohomology modules with respect to the linked ideals

Let $R=\oplus_{n\in \N_0}R_n$ be a standard graded ring, $M$ be a finitely generated graded $R$-module and $R_+:=\oplus_{n\in \N}R_n$ denotes the irrelevant ideal of $R$. In this paper, considering the new concept of linkage of ideals over a module, we study the graded components $H^i_{\fa}(M)_n$ when $\fa$ is an h-linked ideal over $M$. More precisely, we show that $H^i_{\fa}(M)$ is tame in each of the following cases: \begin{itemize} \item [(i)] $i=f_{\fa}^{R_+}(M)$, the first integer $i$ for which $R_+\nsubseteq \sqrt{0:H^i_{\fa}(M)}$; \item [(ii)] $i=\cd(R_+,M)$, the last integer $i$ for which $H^{i}_{R_+}(M)\neq 0$, and $\fa=\fb+R_+$ where $\fb$ is an h-linked ideal with $R_+$ over $M$. \end{itemize} Also, among other things, we describe the components $H^i_{\fa}(M)_n$ where $\fa$ is radically h-$M$-licci with respect to $R_+$ of length 2.

math.AC↗

arXiv2019

Cohomological dimension with respect to the linked ideals

Let $R$ be a commutative Noetherian ring. Using the new concept of linkage of ideals over a module, we show that if $\mathfrak{a}$ is an ideal of $R$ which is linked by the ideal $I$, then $cd(\mathfrak{a},R) \in \{ grad \mathfrak{a}, cd(\fa, H^{grad \mathfrak{a}}_ {\mathfrak{c}} (R)) + grad \mathfrak{a}\}, $ where $\mathfrak{c} : = \bigcap_{\mathfrak{p} \in Ass \frac{R}{I}- V(\mathfrak{a})}\mathfrak{p}$. Also, it is shown that for every ideal $\mathfrak{b}$ which is geometrically linked with $\mathfrak{a},$ $cd(\mathfrak{a}, H^{grad \mathfrak{b}}_ {\mathfrak{b}} (R))$ does not depend on $\mathfrak{b}$

math.AC↗

arXiv2018

Linkage of ideals over a module

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 generalizations of the basic result of Peskine and Szpiro \cite[prop 1.3]{PS}, namely if $R$ is a Gorenstain local ring, $\mathfrak{a} \neq 0$ (an ideal of $R$) and $\mathfrak{b} := 0:_R \mathfrak{a}$ then $\frac{R}{\mathfrak{a}}$ is Cohen-Macaulay if and only if $\frac{R}{\mathfrak{a}}$ is unmixed and $\frac{R}{\mathfrak{b}}$ is Cohen-Macaulay.

math.AC↗

arXiv2018

Attached and Assoiciated Primes Of Local Cohomology Modules Via Linkage

Let $R$ be a commutative Noetherian ring and $M$ be a finitely generated $R$-module. Considering the new concept of linkage of ideals over a module, we study associated prime ideals, cofiniteness and Artinianness of local cohomology modules of $M$ with respect to some linked ideals over it.

math.AC↗

arXiv2018

Characterization of some special rings via linkage

Some descriptions of linked ideals in a commutative Notherian ring $R$ are provided in terms of the Associated prime ideals of $R$. Then, among other things, we make some characterization of Cohen-Macaulay, Gorenstein and regular local rings in terms of their linked ideals.

math.AC↗