Mixed multiplicities of multigraded modules

Việt, Duong Quôc; Manh, Nguyen Tien

doi:10.1515/form.2011.120

Cited by 7 publications

(11 citation statements)

References 18 publications

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“…The notion of filterregular sequences was introduced by Stuckrad and Vogel in [17] (see [2]). The theory of filter-regular sequences became an important tool for studying some classes of singular rings and has been continually developed (see, for example, [2,8,20,29,31] (ii) Let a ∈ S i . Since the following exact sequence…”

Section: Filter-regular Sequences and Mixed Multiplicity Systemsmentioning

confidence: 99%

“…Trung and Verma in 2007 [21] interpreted mixed volumes of polytopes as mixed multiplicities of ideals. Moreover, by using filterregular sequences, Manh and Viet [29] in 2013 characterized mixed multiplicities of multigraded modules in terms of the length of modules. In past years, the theory of mixed multiplicities has attracted much attention and has been continually developed (see, for example, [4,5,[11][12][13][14][15][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]).…”

Section: Introductionmentioning

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%

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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“…The theory of filter-regular sequences became an important tool to study some classes of singular rings and has been continually developed (see e.g. [2,6,18,19,24]). …”

Section: Filter-regular Sequences Of Multi-graded Modulesmentioning

confidence: 99%

“…Note 2.3. If S (1,1,...,1) √ AnnM , then by [24], a homogeneous element x ∈ S is an S ++ -filter-regular element with respect to M if and only if x / ∈ P for any P ∈ Ass S M and P does not contain S ++ . That means x / ∈ S ++ P, P ∈Ass S M P. In this case, for any 1 ≤ i ≤ d, there exists an S ++ -filter-regular element x ∈ S i \ mS i .…”

Section: Filter-regular Sequences Of Multi-graded Modulesmentioning

confidence: 99%