ON THE SECTIONAL GENERA AND COHEN–MACAULAY RINGS

Shinya Kumashiro; Hoang Le Truong; Hoang Ngoc Yen

doi:10.1216/jca.2023.15.577

Abstract

We explore the behavior of the sectional genera of certain primary ideals in Noetherian local rings. We provide characterizations of Cohen–Macaulay local rings in terms of the sectional genera, the Cohen–Macaulay type, and the second Hilbert coefficients for certain primary ideals. We also characterize Gorenstein rings and quasi-Buchsbaum rings in terms of the sectional genera for certain primary ideals.

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Shinya Kumashiro. Hoang Le Truong. Hoang Ngoc Yen. "ON THE SECTIONAL GENERA AND COHEN–MACAULAY RINGS." J. Commut. Algebra 15 (4) 577 - 594, Winter 2023. https://doi.org/10.1216/jca.2023.15.577

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Received: 23 December 2022; Revised: 16 May 2023; Accepted: 6 June 2023; Published: Winter 2023

First available in Project Euclid: 20 December 2023

MathSciNet: MR4680638

Digital Object Identifier: 10.1216/jca.2023.15.577

Subjects:

Primary: 13D40

Secondary: 13H10 , 13H15

Keywords: Cohen–Macaulay , Gorenstein , Hilbert coefficients , quasi-Buchsbaum , sectional genera

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