Multiplicity of the special fiber of blowups

Alberto Corso; Claudia Polini; Wolmer V. Vasconcelos

doi:10.1017/S0305004105009023

Multiplicity of the special fiber of blowups

Alberto Corso, Claudia Polini, Wolmer V. Vasconcelos

Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

Let (R,m) be a local Cohen-Macaulay ring and let I be an m-primary ideal. In this paper we give sharp bounds on the multiplicity of the special fiber ring ℱ of I in terms of other well-known invariants of I. Special attention is then paid in studying when equality holds in these bounds, with a particular interest in the unmixedness or, better, the Cohen-Macaulayness of ℱ.

Original language	English
Pages (from-to)	207-219
Number of pages	13
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	140
Issue number	2
DOIs	https://doi.org/10.1017/S0305004105009023
State	Published - Mar 2006

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Mathematics (all)

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10.1017/S0305004105009023

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title = "Multiplicity of the special fiber of blowups",

abstract = "Let (R,m) be a local Cohen-Macaulay ring and let I be an m-primary ideal. In this paper we give sharp bounds on the multiplicity of the special fiber ring ℱ of I in terms of other well-known invariants of I. Special attention is then paid in studying when equality holds in these bounds, with a particular interest in the unmixedness or, better, the Cohen-Macaulayness of ℱ.",

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AU - Polini, Claudia

AU - Vasconcelos, Wolmer V.

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N2 - Let (R,m) be a local Cohen-Macaulay ring and let I be an m-primary ideal. In this paper we give sharp bounds on the multiplicity of the special fiber ring ℱ of I in terms of other well-known invariants of I. Special attention is then paid in studying when equality holds in these bounds, with a particular interest in the unmixedness or, better, the Cohen-Macaulayness of ℱ.

AB - Let (R,m) be a local Cohen-Macaulay ring and let I be an m-primary ideal. In this paper we give sharp bounds on the multiplicity of the special fiber ring ℱ of I in terms of other well-known invariants of I. Special attention is then paid in studying when equality holds in these bounds, with a particular interest in the unmixedness or, better, the Cohen-Macaulayness of ℱ.

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Multiplicity of the special fiber of blowups

Abstract

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