Reduction Numbers and Multiplicities of Multigraded Structures

Herrmann, Manfred; Hyry, Eero; Ribbe, J.; Tang, Zijie

doi:10.1006/jabr.1997.7128

Cited by 62 publications

(48 citation statements)

References 20 publications

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“…Assume that S 1 √ Ann S M and dim Supp ++ M = s, then by [7,Theorem 4.1], A (M n ) is a polynomial of degree s for all large n. Denote by P M (n) the Hilbert polynomial of the Hilbert function A (M n ). The terms of total degree s in the polynomial P M (n) have the form |k|=s e(M; k)n k /k!.…”

Section: Filter-regular Sequences and Mixed Multiplicity Systemsmentioning

confidence: 99%

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The Euler-Poincaré Characteristic and Mixed Multiplicities

Việt¹,

Thanh²

2015

Kyushu J. Math.

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Abstract. This paper defines mixed multiplicity systems; the Euler-Poincaré characteristic and the mixed multiplicity symbol of N d -graded modules with respect to a mixed multiplicity system, and proves that the Euler-Poincaré characteristic and the mixed multiplicity symbol of any mixed multiplicity system of the type (k 1 , . . . , k d ) and the (k 1 , . . . , k d )-difference of the Hilbert polynomial are the same. As an application, we obtain results for mixed multiplicities.

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Section: Filter-regular Sequences and Mixed Multiplicity Systemsmentioning

confidence: 99%

“…The terms of total degree s in the polynomial P M (n) have the form |k|=s e(M; k)n k /k!. Then e(M; k) are non-negative integers not all zero, called the mixed multiplicity of M of the type k [7]. Now for each k ∈ N d such that |k| ≥ dim Supp ++ M, we put…”

Section: Introductionmentioning

confidence: 99%

The Euler-Poincaré Characteristic and Mixed Multiplicities

Việt¹,

Thanh²

2015

Kyushu J. Math.

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“…In past years, the positivity and the relationship between mixed multiplicities and Hilbert-Samuel multiplicity of ideals have attracted much attention (see e.g. [2,3,4,7,8,9,13,14,17,19,20,21,22,23]). …”

Section: Imentioning

confidence: 99%

A note on joint reductions and mixed multiplicities

Việt

Thanh

2014

Proc. Amer. Math. Soc.

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Let (A, m) be a noetherian local ring with maximal ideal m and infinite residue field k = A/m. Let J be an m-primary ideal, I 1 , . . . , I s ideals of A, and M a finitely generated A-module. In this paper, we interpret mixed multiplicities of (I 1 , . . . , I s , J) with respect to M as multiplicities of joint reductions of them. This generalizes the Rees's theorem on mixed multiplicity [12, Theorem 2.4]. As an application we show that mixed multiplicities are also multiplicities of Rees's superficial sequences.

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“…If ht I + AnnN AnnN > 0, then e M is the sum of all the mixed multiplicities of M by [4,20]. Hence e M = e M .…”

Section: Multiplicity Of Multi-graded Rees Modulesmentioning

confidence: 99%

“…. , k d ) of M [4]. In the case that (R, n) is a noetherian local ring with maximal ideal n, J is an nprimary ideal, I 1 , .…”

mentioning

confidence: 99%