On the sectional genera and Cohen-Macaulay rings
Commutative Algebra
2022-06-13 v1
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.
Keywords
Cite
@article{arxiv.2206.04859,
title = {On the sectional genera and Cohen-Macaulay rings},
author = {Shinya Kumashiro and Hoang Le Truong and Hoang Ngoc Yen},
journal= {arXiv preprint arXiv:2206.04859},
year = {2022}
}
Comments
14 pages. Comments welcome!