2025/06/25 by Dawn, Biplab, Saloni, Kumari
#13D45 #13F65 #13H10 #14B15 #14H20 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2506.20473
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≥ 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≥ 1. We also discuss Castelnuovo-Mumford regularity of certain curves in terms of k-Buchsbaumness.