Integral closedness of MI and the formula of Hoskin and Deligne for finitely supported complete ideals

D'Cruz, Clare

doi:10.1016/j.jalgebra.2005.08.028

Cited by 6 publications

(5 citation statements)

References 28 publications

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“…Let I be an m-primary complete ideal in a 2-dimensional regular local ring (R, m). We say that a The Hoskin-Deligne formula has been generalized for finitely supported mprimary ideals in regular local rings of dimension at least three by C. D'Cruz [7]. B. Johnston [22] established a multiplicity formula for the same class of ideals.…”

Section: Normal Hilbert Polynomials In Two Dimensional Regular Local ...mentioning

confidence: 99%

Normal Hilbert Polynomials : A survey

Mandal¹,

Masuti²,

Verma³

2012

Preprint

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We survey some of the major results about normal Hilbert polynomials of ideals. We discuss a formula due to Lipman for complete ideals in regular local rings of dimension two, theorems of Huneke, Itoh, Huckaba, Marley and Rees in Cohen-Macaulay analytically unramified local rings. We also discuss recent works of Goto-Hong-Mandal and Mandal-Singh-Verma concerning the positivity of the first coefficient of the normal Hilbert polynomial in unmixed analytically unramified local rings. Results of Moralés and Villarreal linking normal Hilbert polynomial of monomial ideals with Ehrhart polynomials of polytopes are also presented. Contents 14 5. Study of e 3 (I) 19 6. Normal Hilbert Polynomials in two dimensional regular local rings 25 7. The normal Hilbert polynomial of a monomial ideal 30 References 33

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Section: Normal Hilbert Polynomials In Two Dimensional Regular Local ...mentioning

confidence: 99%

Normal Hilbert Polynomials : A survey

Mandal¹,

Masuti²,

Verma³

2012

Preprint

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“…In general, even for a normal ideal I the product mI need not be integrally closed, see [DC2,Example 7.1].…”

Section: It Follows Thatmentioning

confidence: 99%

“…Special cases of Theorem 3.18 and Proposition 3.19 appear in [DC1]. In general, even for a normal ideal I the product mI need not be integrally closed, see [DC2,Example 7.1]. Proposition 3.19.…”

Section: We Havementioning

confidence: 99%

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Integrally closed and componentwise linear ideals

2009

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Abstract. In a two dimensional regular local ring integrally closed ideals have a unique factorization property and their associated graded ring is CohenMacaulay. In higher dimension these properties do not hold and the goal of the paper is to identify a subclass of integrally closed ideals for which they do. We restrict our attention to 0-dimensional homogeneous ideals in polynomial rings R of arbitrary dimension. We identify a class of integrally closed ideals, the Goto-class G * , which is closed under product and it has a suitable unique factorization property. Ideals in G * have a Cohen-Macaulay associated graded ring if either they are monomial or dim R ≤ 3. Our approach is based on the study of the relationship between the notions of integrally closed, contracted, full and componentwise linear ideals.

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“…is true for clusters are investigated in homological terms in [19]. If C is a configuration, as in the case of constellations, σ C : X C → X will denote the composition of the blowing-ups of all the points in C; moreover two configurations C and C ′ over X are identified if there exist an automorphism π of X and an isomorphism π ′ :…”

Section: Characteristic Cones Of Toric Constellationsmentioning

confidence: 99%