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

Abstract Given a homogeneous ideal I ⊂ K [ x 0 ,…, x n ] defining a subscheme X of projective n -space P K n , we provide an effective method to compute the Castelnuovo–Mumford regularity of X in the following two cases: when X is arithmetically Cohen–Macaulay, and when X is a not necessarily reduced projective curve. In both cases, we compute the Castelnuovo–Mumford regularity of X by means of quotients of zero-dimensional monomial ideals.