On the notion of sequentially Cohen–Macaulay modules

Caviglia, Giulio; Stefani, Alessandro De; Sbarra, Enrico; Strazzanti, Francesco

doi:10.1007/s40687-022-00332-4

Cited by 3 publications

(1 citation statement)

References 35 publications

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“…We refer the interested reader to see [CDSSS22] for motivations to study on the concept of sequentially Cohen-Macaulay modules. In [SS17], the authors introduced the following notion: Definition 4.5.…”

Section: Lyubeznik Tablesmentioning

confidence: 99%

Certain endomorphism rings of local cohomology modules and Lyubeznik numbers

Boix¹,

Eghbali²

2022

Preprint

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The goal of this paper is twofold; on the one hand, motivated by questions raised by Schenzel, we explore situations where the Hartshorne-Lichtenbaum Vanishing Theorem for local cohomology fails, leading us to simpler expressions of certain local cohomology modules. As application, we give new expressions of the endomorphism ring of these modules. On the other hand, building upon previous work by Àlvarez Montaner, we exhibit the shape of Lyubeznik tables of the so-called partially sequentially Cohen-Macaulay rings as introduced by Sbarra and Strazzanti.

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Section: Lyubeznik Tablesmentioning

confidence: 99%

Certain endomorphism rings of local cohomology modules and Lyubeznik numbers

Boix¹,

Eghbali²

2022

Preprint

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A criterion for sequential Cohen-Macaulayness

Caviglia,

De Stefani

2024

Arch. Math.

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The purpose of this note is to show that a finitely generated graded module M over $$S=k[x_1,\ldots ,x_n]$$ S = k [ x 1 , … , x n ] , k a field, is sequentially Cohen-Macaulay if and only if its arithmetic degree $${\text {adeg}}(M)$$ adeg ( M ) agrees with $${\text {adeg}}(F/{\text {gin}}_\textrm{revlex}(U))$$ adeg ( F / gin revlex ( U ) ) , where F is a graded free S-module and $$M \cong F/U$$ M ≅ F / U . This answers positively a conjecture of Lu and Yu from 2016.

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Certain endomorphism rings of local cohomology modules and Lyubeznik numbers

Boix

Eghbali

2023

Int. J. Algebra Comput.

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The goal of this paper is twofold: on the one hand, motivated by questions raised by Schenzel, we explore situations where the Hartshorne–Lichtenbaum Vanishing theorem for local cohomology fails, leading us to simpler expressions of certain local cohomology modules. As application, we give new expressions of the endomorphism ring of these modules. On the other hand, building upon previous work by Àlvarez Montaner, we exhibit the shape of Lyubeznik tables of the so-called partially sequentially Cohen–Macaulay rings as introduced by Sbarra and Strazzanti.

show abstract

On the notion of sequentially Cohen–Macaulay modules

Cited by 3 publications

References 35 publications

Certain endomorphism rings of local cohomology modules and Lyubeznik numbers

Certain endomorphism rings of local cohomology modules and Lyubeznik numbers

A criterion for sequential Cohen-Macaulayness

Certain endomorphism rings of local cohomology modules and Lyubeznik numbers

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