Buchsbaumness and Castelnuovo-Mumford regularity of non-smooth monomial curves

TL;DR

This paper characterizes the Buchsbaumness and Castelnuovo-Mumford regularity of projective monomial curves using their finite Macaulayfication, providing new insights into the algebraic properties of non-smooth monomial curves.

Contribution

It introduces a method to determine Buchsbaumness and estimate regularity of non-smooth monomial curves via Macaulayfication, advancing understanding of their algebraic structure.

Findings

Characterization of Buchsbaumness using Macaulayfication

Estimation of Castelnuovo-Mumford regularity for classes of monomial curves

Application of the method to non-smooth monomial curves

Abstract

Projective monomial curves correspond to rings generated by monomials of the same degree in two variables. Such rings always have finite Macaulayfication. We show how to characterize the Buchsbaumness and the Castelnuovo-Mumford regularity of these rings by means of their finite Macaulayfication, and we use this method to study the Buchsbaumness and to estimate the Castelnuovo-Mumford regularity of large classes of non-smooth monomial curves in terms of the given monomials.