Hilbert coefficients of ideals with a view toward blowup algebras

Alberto Corso; Claudia Polini

doi:10.1201/9781420050912

Hilbert coefficients of ideals with a view toward blowup algebras

Alberto Corso, Claudia Polini

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

2.1 Introduction Our basic object of study is a Cohen-Macaulay local ring (R, m) of dimension d and its R-ideals. The examination of the asymptotic properties of such ideals has evolved into a challenging area of research, touching most aspects of commutative algebra, including its interaction with computational algebra and algebraic geometry. It takes expression in several graded algebras attached to I, among which we single out the Rees algebra R[It], the associated graded ring gr_I(R) and the special fiber ring F(I) of I; namely, R[It] = ^∞⊕_k=0 I^kt^k, gr_I (R) = R[It]/IR[It], F(I) = R[It]/mR[It].

Original language	English
Title of host publication	Syzygies and Hilbert Functions
Pages	41-65
Number of pages	25
ISBN (Electronic)	9781420050912
DOIs	https://doi.org/10.1201/9781420050912
State	Published - Jan 1 2007

Bibliographical note

Publisher Copyright:
© 2007 by Taylor & Francis Group, LLC.

ASJC Scopus subject areas

General Mathematics

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10.1201/9781420050912

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abstract = "2.1 Introduction Our basic object of study is a Cohen-Macaulay local ring (R, m) of dimension d and its R-ideals. The examination of the asymptotic properties of such ideals has evolved into a challenging area of research, touching most aspects of commutative algebra, including its interaction with computational algebra and algebraic geometry. It takes expression in several graded algebras attached to I, among which we single out the Rees algebra R[It], the associated graded ring grI(R) and the special fiber ring F(I) of I; namely, R[It] = ∞⊕k=0 Iktk, grI (R) = R[It]/IR[It], F(I) = R[It]/mR[It].",

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AB - 2.1 Introduction Our basic object of study is a Cohen-Macaulay local ring (R, m) of dimension d and its R-ideals. The examination of the asymptotic properties of such ideals has evolved into a challenging area of research, touching most aspects of commutative algebra, including its interaction with computational algebra and algebraic geometry. It takes expression in several graded algebras attached to I, among which we single out the Rees algebra R[It], the associated graded ring grI(R) and the special fiber ring F(I) of I; namely, R[It] = ∞⊕k=0 Iktk, grI (R) = R[It]/IR[It], F(I) = R[It]/mR[It].

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BT - Syzygies and Hilbert Functions

ER -

Hilbert coefficients of ideals with a view toward blowup algebras

Abstract

Bibliographical note

ASJC Scopus subject areas

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