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Nearly Gorenstein local rings defined by maximal minors of a $2 \times n$ matrix

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arxiv 2308.04234 v1 pith:TAESE73D submitted 2023-08-08 math.AC

Shinya Kumashiro , Naoyuki Matsuoka , Taiga Nakashima This is my paper · ORCID
classification math.AC
keywords gorensteinnearlydefinedlocalmatrixmaximalminorsring
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abstract

We investigate the nearly Gorenstein property of a local ring defined by the maximal minors of a specific $2 \times n$ matrix with entries in the formal power series ring $k[[X_1, X_2, \ldots , X_n]]$ over a field $k$. Our findings allow us to present numerous concrete examples, such as nearly Gorenstein rings that are not almost Gorenstein and vice versa.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Trace ideals, conductors, and ideals of finite (phantom) projective dimension

    math.AC 2025-01 conditional novelty 8.0 of 10

    The paper unifies and extends several non-containment results for trace and test ideals, and answers an open question of Huneke-Swanson with an explicit counterexample.

  2. The canonical trace of Stanley-Reisner rings that are Gorenstein on the punctured spectrum

    math.AC 2024-12 conditional novelty 6.0 of 10

    Nearly Gorenstein Stanley-Reisner rings of dimension at least three are Gorenstein, and canonical traces of punctured-Gorenstein Stanley-Reisner rings are exactly the ring, the maximal ideal, or its square.

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