Residual intersections and modules with Cohen-Macaulay Rees algebra

Costantini, Alessandra

doi:10.1016/j.jalgebra.2021.07.022

Cited by 3 publications

(1 citation statement)

References 38 publications

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“…Since R is Gorenstein, the assumption that depth(E j ) ≥ d − j for every 1 ≤ j ≤ ℓ − e implies that Ext j+1 R (E j , R) = 0 for all j in the same range. Moreover, from [11,Theorem 4.3] it follows that R(E) is Cohen-Macaulay. Then, all assumptions of Theorem 4.3 are satisfied, whence the remaining statements follow.…”

Section: Core Of Modulesmentioning

confidence: 99%

Residual Intersections and Core of Modules

Costantini¹,

Fouli²,

Hong³

2022

Preprint

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We introduce the notion of residual intersections of modules and prove their existence. We show that projective dimension one modules have Cohen-Macaulay residual intersections, namely they satisfy the relevant Artin-Nagata property. We then establish a formula for the core of orientable modules satisfying certain homological conditions, extending previous results of Corso, Polini, and Ulrich on the core of projective one modules. Finally, we provide examples of classes of modules that satisfy our assumptions.

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Section: Core Of Modulesmentioning

confidence: 99%

Residual Intersections and Core of Modules

Costantini¹,

Fouli²,

Hong³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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Residual intersections and core of modules

2023

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On the Cohen-Macaulay property of the Rees algebra of the module of differentials

Costantini

Dang

2021

Proc. Amer. Math. Soc.

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Let R R be an algebra essentially of finite type over a field k k and let Ω k ( R ) \Omega _k(R) be its module of Kähler differentials over k k . If R R is a homogeneous complete intersection and c h a r ( k ) = 0 \mathrm {char}(k)=0 , we prove that Ω k ( R ) \Omega _k(R) is of linear type whenever its Rees algebra is Cohen-Macaulay and locally at every non-maximal homogeneous prime p \mathfrak {p} the embedding dimension of R p R_{\mathfrak {p}} is at most twice its dimension. This improves a previous result of Simis, Ulrich and Vasconcelos for the module of differentials of a ring that is locally a complete intersection, in which case the latter condition is assumed locally at every prime.

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Residual intersections and modules with Cohen-Macaulay Rees algebra

Cited by 3 publications

References 38 publications

Residual Intersections and Core of Modules

Residual Intersections and Core of Modules

Residual intersections and core of modules

On the Cohen-Macaulay property of the Rees algebra of the module of differentials

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