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arXiv · 2206.04859

On the sectional genera and Cohen-Macaulay rings

Shinya Kumashiro·Hoang Le Truong·Hoang Ngoc Yen
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Abstract

We explore the behavior of the sectional genera of certain primary ideals in Noetherian local rings. In this paper, we provide characterizations of a Cohen-Macaulay local ring 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. 2022-06-10. On the sectional genera and Cohen-Macaulay rings. https://arxiv.org/abs/2206.04859

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