ON THE STABILITY AND REGULARITY OF THE MULTIPLIER IDEALS OF MONOMIAL IDEALS

Let a subset of C[x(1),..., x(d)] be a monomial ideal and J(a) its multiplier ideal which is also a monomial ideal. It is proved that if a is strongly stable or squarefree strongly stable then so is J (a). Denote the maximal degree of minimal generators of a by d(a). When a is strongly stable or squarefree strongly stable, it is shown that the Castelnuovo-Mumford regularity of J (a) is less than or equal to d (a). As a corollary, one gets a vanishing result on the ideal sheaf<(J(a))over tilde> on P-d (1) associated to J (a) that H-i (Pd-1; <(J(a))over tilde> (s - i)) = 0, for all i > 0 and s >= d (a).