Noether resolutions in dimension 2

As an application of the results for 2-dimensional semigroup rings, we provide a new upper bound for the Castelnuovo-Mumford regularity of the coordinate ring of a projective monomial curve. Finally, we describe the multigraded Noether resolution and the Macaulayfication of either the coordinate ring of a projective monomial curve C⊆PKn associated to an arithmetic sequence or the coordinate ring of any canonical projection πr(C) of C to PKn−1.