On the Symmetric and Rees Algebras of Certain Determinantal Ideals

Fukumuro, Kosuke

doi:10.3836/tjm/1406552444

Cited by 2 publications

(2 citation statements)

References 3 publications

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“…, f m )S ⊆ Ker π . For our purpose, the following result due to Avramov [1] is very important (Another elementary proof is given in [3]). As the last preliminary result, we describe a technique using determinants of matrices.…”

Section: Preliminariesmentioning

confidence: 99%

Saturations of powers of certain determinantal ideals

Fukumuro¹,

Inagawa²,

Nishida³

2015

J. Commut. Algebra

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Let R be a Noetherian local ring and m a positive integer. Let I be the ideal of R generated by the maximal minors of an m × (m + 1) matrix M with entries in R . Assuming that the grade of the ideal generated by the k-minors of M is at least m − k + 2 for 1 ≤ ∀k ≤ m , we will study the associated primes of I n for ∀n > 0 . Moreover, we compute the saturation of I n for 1 ≤ ∀n ≤ m in the case where R is a Cohen-Macaulay ring and the entries of M are powers of elements that form an sop for R .

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Section: Preliminariesmentioning

confidence: 99%

Saturations of powers of certain determinantal ideals

Fukumuro¹,

Inagawa²,

Nishida³

2015

J. Commut. Algebra

Self Cite

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“…The second part of this chapter, where we use the results of (AVRAMOV, 1981) and (FUKUMURO;KUME;NISHIDA, 2015), is motivated to find a class of modules that satisfy the (SW j ) condition. Here we can verify that modules of projective dimension 1 and that are of linear type, that is, their Rees Algebra is isomorphic to its Symmetric Algebra, satisfy the (SW j ) condition for all j = 1, .…”

Section: Introductionmentioning

confidence: 99%

On Betti numbers for symmetric powers of modules and some applications

Lima¹

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Seja M um módulo finitamente gerado sobre um anel local (R, m). Por S j (M), denotamos a j-ésima potência simétrica de M( j-ésima componente graduada da álgebra simétrica S R (M)).O propósito desta tese é investigar a resolução livre minimal de S j (M) como R-módulo para cada j ≥ 2 e determinar os números de Betti de S j (M) em termos dos números de Betti de M. Isso tem algumas aplicações, por exemplo para ideais de tipo linear I, obtemos fórmulas dos números de Betti de I j em termos dos números de Betti de I. Além disso, estabelecemos cotas superiores e inferiores para os números de Betti de S j (M) em termos dos números de Betti de M. Em particular, obtemos algumas aplicações sobre a famosa conjectura de Buchsbaum-Eisenbud-Horrocks.

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On the Symmetric and Rees Algebras of Certain Determinantal Ideals

Cited by 2 publications

References 3 publications

Saturations of powers of certain determinantal ideals

Saturations of powers of certain determinantal ideals

On Betti numbers for symmetric powers of modules and some applications

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