On cohomological dimension and depth under linkage

Eghbali, Majid; Shirmohammadi, N.

doi:10.1080/00927872.2016.1175598

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Cited by 4 publications

(1 citation statement)

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“…As zd(R/I) = p∈AssR(R/I) p, we observe that m zd(R/I) (m is not contained in the zero divisors of R/I), that is H 0 m (R/I) = 0. From the exact sequence (6.1), one has depth K R/J − 1 = depth R/I (for detailed proof see [6,Proposition 3.3]). It implies that depth K R/J > 1. once again, in the light of (6.1) we have Then, If I is set-theoretically Cohen-Macaulay then so is J.…”

Section: Linkagementioning

confidence: 99%

Vanishing of local cohomology and set-theoretically Cohen-Macaulay ideals

Eghbali¹,

Boix²

2018

Preprint

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In this paper, first, we generalize a result of Peskine-Szpiro on the relation between the cohomological dimension and projective dimension.Then, we give conditions for the vanishing of local cohomology from local to global and vice versa. Our final goal in the present paper is examining the set-theoretically Cohen-Macaulay ideals to find some cohomological characterization of these kinds of ideals.

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Section: Linkagementioning

confidence: 99%

Vanishing of local cohomology and set-theoretically Cohen-Macaulay ideals

Eghbali¹,

Boix²

2018

Preprint

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Vanishing of local cohomology and set-theoretically Cohen–Macaulay ideals

Eghbali¹

2022

Rend. Circ. Mat. Palermo, II. Ser

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Lyubeznik tables of linked ideals

2019

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In this paper, we examine the Lyubeznik tables of two linked ideals [Formula: see text] and [Formula: see text] of a complete regular local ring [Formula: see text] containing a field. More precisely, we prove that the Lyubeznik tables of two evenly linked ideals [Formula: see text] and [Formula: see text] are the same when [Formula: see text] and [Formula: see text] both satisfy one of the following properties: (1) canonically Cohen–Macaulay, (2) generalized Cohen–Macaulay and (3) Buchsbaum. Furthermore, we give some conditions for equality of Lyubeznik tables of two linked ideals of dimension 2.

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On cohomological dimension and depth under linkage

Abstract: ABSTRACT. Some relations between cohomological dimensions and depths of linked ideals are investigated and discussed by various examples.

Cited by 4 publications

References 20 publications

Vanishing of local cohomology and set-theoretically Cohen-Macaulay ideals

Vanishing of local cohomology and set-theoretically Cohen-Macaulay ideals

Vanishing of local cohomology and set-theoretically Cohen–Macaulay ideals

Lyubeznik tables of linked ideals

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