Buchsbaumness and Castelnuovo-Mumford regularity of 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.