Kyoto Journal of Mathematics

On the almost Gorenstein property in the Rees algebras of contracted ideals

Shiro Goto, Naoyuki Matsuoka, Naoki Taniguchi, and Ken-ichi Yoshida

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Abstract

We explore the question of when the Rees algebra R(I)=n0In of I is an almost Gorenstein graded ring, where R is a 2-dimensional regular local ring and I is a contracted ideal of R. Recently, we showed that R(I) is an almost Gorenstein graded ring for every integrally closed ideal I of R. The main results of the present article show that if I is a contracted ideal with o(I)2, then R(I) is an almost Gorenstein graded ring, while if o(I)3, then R(I) is not necessarily an almost Gorenstein graded ring, even though I is a contracted stable ideal. Thus both affirmative and negative answers are given.

Article information

Source
Kyoto J. Math., Volume 59, Number 4 (2019), 769-785.

Dates
Received: 26 August 2016
Revised: 1 June 2017
Accepted: 8 June 2017
First available in Project Euclid: 24 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1571904147

Digital Object Identifier
doi:10.1215/21562261-2018-0001

Mathematical Reviews number (MathSciNet)
MR4032199

Zentralblatt MATH identifier
07193997

Subjects
Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
Secondary: 13H15: Multiplicity theory and related topics [See also 14C17] 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics

Keywords
almost Gorenstein local ring almost Gorenstein graded ring Rees algebra contracted ideal

Citation

Goto, Shiro; Matsuoka, Naoyuki; Taniguchi, Naoki; Yoshida, Ken-ichi. On the almost Gorenstein property in the Rees algebras of contracted ideals. Kyoto J. Math. 59 (2019), no. 4, 769--785. doi:10.1215/21562261-2018-0001. https://projecteuclid.org/euclid.kjm/1571904147


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