Constructing homogeneous Gorenstein ideals

Sema Güntürkün; Uwe Nagel

doi:10.1016/j.jalgebra.2013.11.015

Constructing homogeneous Gorenstein ideals

Sema Güntürkün
, Uwe Nagel

Mathematics

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

2 Scopus citations

Abstract

In 1983 Kustin and Miller introduced a construction of Gorenstein ideals in local Gorenstein rings, starting from smaller such ideals. We review and modify their construction in the case of graded rings and discuss it within the framework of Gorenstein liaison theory. We determine invariants of the constructed ideal. Concerning the problem of when a given Gorenstein ideal can be obtained by the construction, we derive a necessary condition and exhibit a Gorenstein ideal that cannot be obtained using the construction.

Original language	English
Pages (from-to)	107-124
Number of pages	18
Journal	Journal of Algebra
Volume	401
DOIs	https://doi.org/10.1016/j.jalgebra.2013.11.015
State	Published - Mar 1 2014

Bibliographical note

Funding Information:
Part of the work for this paper was done while the second author was partially supported by the National Security Agency under Grant Number H98230-12-1-0247 .

Funding

Part of the work for this paper was done while the second author was partially supported by the National Security Agency under Grant Number H98230-12-1-0247 .

Funders	Funder number
National Security Agency	H98230-12-1-0247

Keywords

Elementary biliaison
Free resolution
Gorenstein ideal
Liaison

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2013.11.015

Cite this

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title = "Constructing homogeneous Gorenstein ideals",

abstract = "In 1983 Kustin and Miller introduced a construction of Gorenstein ideals in local Gorenstein rings, starting from smaller such ideals. We review and modify their construction in the case of graded rings and discuss it within the framework of Gorenstein liaison theory. We determine invariants of the constructed ideal. Concerning the problem of when a given Gorenstein ideal can be obtained by the construction, we derive a necessary condition and exhibit a Gorenstein ideal that cannot be obtained using the construction.",

keywords = "Elementary biliaison, Free resolution, Gorenstein ideal, Liaison",

author = "Sema G{\"u}nt{\"u}rk{\"u}n and Uwe Nagel",

note = "Funding Information: Part of the work for this paper was done while the second author was partially supported by the National Security Agency under Grant Number H98230-12-1-0247 . ",

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AU - Güntürkün, Sema

AU - Nagel, Uwe

N1 - Funding Information: Part of the work for this paper was done while the second author was partially supported by the National Security Agency under Grant Number H98230-12-1-0247 .

PY - 2014/3/1

Y1 - 2014/3/1

N2 - In 1983 Kustin and Miller introduced a construction of Gorenstein ideals in local Gorenstein rings, starting from smaller such ideals. We review and modify their construction in the case of graded rings and discuss it within the framework of Gorenstein liaison theory. We determine invariants of the constructed ideal. Concerning the problem of when a given Gorenstein ideal can be obtained by the construction, we derive a necessary condition and exhibit a Gorenstein ideal that cannot be obtained using the construction.

AB - In 1983 Kustin and Miller introduced a construction of Gorenstein ideals in local Gorenstein rings, starting from smaller such ideals. We review and modify their construction in the case of graded rings and discuss it within the framework of Gorenstein liaison theory. We determine invariants of the constructed ideal. Concerning the problem of when a given Gorenstein ideal can be obtained by the construction, we derive a necessary condition and exhibit a Gorenstein ideal that cannot be obtained using the construction.

KW - Elementary biliaison

KW - Free resolution

KW - Gorenstein ideal

KW - Liaison

UR - https://www.scopus.com/pages/publications/84891365595

UR - https://www.scopus.com/pages/publications/84891365595#tab=citedBy

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DO - 10.1016/j.jalgebra.2013.11.015

M3 - Article

AN - SCOPUS:84891365595

SN - 0021-8693

VL - 401

SP - 107

EP - 124

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Constructing homogeneous Gorenstein ideals

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this