Minkowski inequality and equality for
                    multiplicity of ideals of finite length in
                    Noetherian local rings

Goel, Kriti; Gurjar, R. V.; Verma, J. K.

doi:10.1090/conm/738/14877

Cited by 6 publications

(2 citation statements)

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“…The development of the subject of mixed multiplicities and its connection to Teissier's work on equisingularity [21] can be found in [8]. A survey of the theory of mixed multiplicities of ideals can be found in [20, Chapter 17], including discussion of the results of the papers of Rees [17] and of Swanson [19], and the theory of Minkowski inequalities of Teissier [21, 22], Rees and Sharp [18] and Katz [10].…”

Section: Introductionmentioning

confidence: 99%

Positivity of mixed multiplicities of filtrations

Cutkosky

Srinivasan

Verma

2020

Bull. London Math. Soc.

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The theory of mixed multiplicities of filtrations by m-primary ideals in a ring is introduced in [Cutkosky, P. Sarkar and H. Srinivasan, Trans. Amer. Math. Soc. 372 (2019) 6183-6211]. In this paper, we consider the positivity of mixed multiplicities of filtrations. We show that the mixed multiplicities of filtrations must be nonnegative real numbers and give examples to show that they could be zero or even irrational. When R is analytically irreducible, and I(1), . . . , I(r) are filtrations of R by mR-primary ideals, we show that all of the mixed multiplicities eR (I(1) [d 1 ] , . . . , I(r) [dr ] ; R) are positive if and only if the ordinary multiplicities eR(I(i); R) for 1 i r are positive. We extend this to modules and prove a simple characterization of when the mixed multiplicities are positive or zero on a finitely generated module.

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Section: Introductionmentioning

confidence: 99%

Positivity of mixed multiplicities of filtrations

Cutkosky

Srinivasan

Verma

2020

Bull. London Math. Soc.

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“…The development of the subject of mixed multiplicities and its connection to Teissier's work on equisingularity [37] can be found in [18]. A survey of the theory of mixed multiplicities of ideals can be found in [36,Chapter 17], including discussion of the results of the papers [31] of Rees and [35] of Swanson, and the theory of Minkowski inequalities of Teissier [37], [38], Rees and Sharp [34] and Katz [21].…”

Section: Introductionmentioning

confidence: 99%

The Minkowski Equality for Filtrations

Cutkosky¹

2020

Preprint

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Suppose that R is an analytically irreducible or excellent local domain with maximal ideal mR. We consider multiplicities and mixed multiplicities of R by filtrations of mR-primary ideals. We show that the theorem of Teissier, Rees and Sharp, and Katz, characterizing equality in the Minkowski inequality for multiplicities of ideals, is true for divisorial filtrations, and for the larger category of bounded filtrations. This theorem is not true for arbitrary filtrations of mR-primary ideals.

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Multiplicities and mixed multiplicities of arbitrary filtrations

Cutkosky

Sarkar

2022

Res Math Sci

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Minkowski inequality and equality for multiplicity of ideals of finite length in Noetherian local rings

Cited by 6 publications

References 0 publications

Positivity of mixed multiplicities of filtrations

Positivity of mixed multiplicities of filtrations

The Minkowski Equality for Filtrations

Multiplicities and mixed multiplicities of arbitrary filtrations

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