Reductions and Mixed Multiplicities of Ideals

Việt, Duong Quôc

doi:10.1081/agb-200034021

Cited by 11 publications

(13 citation statements)

References 13 publications

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“…The proof of (ii) is based on the idea in the proof of [21,Theorem 3.4]. We first show by induction on m that (y 1 , .…”

Section: Definition 21 ([18]mentioning

confidence: 99%

“…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%

“…And he proved that mixed multiplicities of m-primary ideals are multiplicities of ideals generated by joint reductions. This concept was extended to the set of arbitrary ideals by [9,11,21].…”

Section: Definition 21 ([18]mentioning

confidence: 99%

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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 proof of (ii) is based on the idea in the proof of [21,Theorem 3.4]. We first show by induction on m that (y 1 , .…”

Section: Definition 21 ([18]mentioning

confidence: 99%

Section: Imentioning

confidence: 99%

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A note on joint reductions and mixed multiplicities

Việt

Thanh

2014

Proc. Amer. Math. Soc.

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“…[7,8,9,11,14,16,19,21,22,23,25]). In past years, using different sequences, one expressed mixed multiplicities into Hilbert-Samuel multiplicity, for instance: Risler-Teissier in 1973 [17] by superficial sequences and Rees in 1984 [13] by joint reductions; Viet in 2000 [21] by (FC)-sequences (see e.g.…”

Section: Filter-regular Sequences Of Multi-graded Modulesmentioning

confidence: 99%

On some multiplicity and mixed multiplicity formulas

Việt

Thanh

2011

Forum Mathematicum

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“…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%

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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Reductions and Mixed Multiplicities of Ideals

Cited by 11 publications

References 13 publications

A note on joint reductions and mixed multiplicities

A note on joint reductions and mixed multiplicities

On some multiplicity and mixed multiplicity formulas

The Euler-Poincaré Characteristic and Mixed Multiplicities

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