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Mathematics > Commutative Algebra

arXiv:2206.00552 (math)
[Submitted on 1 Jun 2022 (v1), last revised 26 Jan 2023 (this version, v8)]

Title:Levelness versus nearly Gorensteinness of homogeneous domains

Authors:Sora Miyashita
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Abstract:Levelness and nearly Gorensteinness are well-studied properties of graded rings as a generalized notion of Gorensteinness. In this paper, we compare the strength of these properties. For any Cohen-Macaulay homogeneous affine semigroup ring R, we give a necessary condition for R to be non-Gorenstein and nearly Gorenstein in terms of the h-vector of R and we show that if R is nearly Gorenstein with Cohen-Macaulay type 2, then it is level. We also show that if Cohen-Macaulay type is more than 2, there are 2-dimensional counterexamples. Moreover, we characterize nearly Gorensteinness of Stanley-Reisner rings of low-dimensional simplicial complexes.
Comments: 17 pages
Subjects: Commutative Algebra (math.AC)
MSC classes: 13H10 (Primary), 13M05 (Secondary)
Cite as: arXiv:2206.00552 [math.AC]
  (or arXiv:2206.00552v8 [math.AC] for this version)
  https://doi.org/10.48550/arXiv.2206.00552

Submission history

From: Sora Miyashita [view email]
[v1] Wed, 1 Jun 2022 15:05:24 UTC (10 KB)
[v2] Thu, 2 Jun 2022 05:28:42 UTC (10 KB)
[v3] Sun, 5 Jun 2022 04:02:41 UTC (10 KB)
[v4] Thu, 11 Aug 2022 14:25:24 UTC (14 KB)
[v5] Fri, 12 Aug 2022 12:48:14 UTC (14 KB)
[v6] Sun, 13 Nov 2022 09:55:30 UTC (16 KB)
[v7] Wed, 25 Jan 2023 06:25:34 UTC (17 KB)
[v8] Thu, 26 Jan 2023 01:50:40 UTC (17 KB)
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