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arXiv · 2506.20473

Buchsbaumness, Macaulayfication and Castelnuovo-Mumford regularity of monomial curves

Biplab Dawn·Kumari Saloni
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Abstract

Projective monomial curves are associated with rings generated by monomials of equal degree in two variables. In this paper, we give an infinite class of non-smooth, non Cohen-Macaulay $k$-Buchsbaum projective monomial curves for any $k\geq 1$ and find the monomial generators for the respective Macaulayfication. More generally, we demonstrate a method to find the Macaulayfication of a $k$-Buchsbaum monomial curve for any $k\geq 1$. We also discuss Castelnuovo-Mumford regularity of certain curves in terms of $k$-Buchsbaumness.

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Biplab Dawn, Kumari Saloni. 2025-06-25. Buchsbaumness, Macaulayfication and Castelnuovo-Mumford regularity of monomial curves. https://arxiv.org/abs/2506.20473

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