In this paper we present a method to find the regularity of projective monomial curves in terms of an ordering of monoids associated to them. We use this result to find the regularity of certain monomial curves and investigate where regularity is attained in their minimal graded free resolutions.
"On the regularity of certain projective monomial curves." Illinois J. Math. 54 (2) 501 - 508, Summer 2010. https://doi.org/10.1215/ijm/1318598670