Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 59, Number 4 (2019), 769-785.
On the almost Gorenstein property in the Rees algebras of contracted ideals
We explore the question of when the Rees algebra of is an almost Gorenstein graded ring, where is a 2-dimensional regular local ring and is a contracted ideal of . Recently, we showed that is an almost Gorenstein graded ring for every integrally closed ideal of . The main results of the present article show that if is a contracted ideal with , then is an almost Gorenstein graded ring, while if , then is not necessarily an almost Gorenstein graded ring, even though is a contracted stable ideal. Thus both affirmative and negative answers are given.
Kyoto J. Math., Volume 59, Number 4 (2019), 769-785.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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