Computing the Castelnuovo–Mumford regularity of some subschemes of image using quotients of monomial ideals

Given a homogeneous ideal Isubset ofK[x0,…,xn] defining a subscheme image of projective n-space image, we provide an effective method to compute the Castelnuovo–Mumford regularity of image in the following two cases: when image is arithmetically Cohen–Macaulay, and when image is a not necessarily reduced projective curve. In both cases, we compute the Castelnuovo–Mumford regularity of image by means of quotients of zero-dimensional monomial ideals.