On the symmetric and Rees algebras of certain determinantal ideals

Fukumuro, Kosuke

doi:10.48550/arxiv.1306.0993

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2015

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“…For our purpose, the following result due to Avramov [1] is very important (Another elementary proof is given in [3]).…”

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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“…For our purpose, the following result due to Avramov [1] is very important (Another elementary proof is given in [3]).…”

Section: Preliminariesmentioning

confidence: 99%