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

AbstractGiven a homogeneous ideal I⊂K[x0,…,xn] defining a subscheme X of projective n-space PKn, 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