Abstract
Let I be an ideal whose symbolic Rees algebra is Noetherian. For m >= 1, the m-th symbolic defect, sdefect(I, m), of I is defined to be the minimal number of generators of the module I-(m)/I-(m). We prove that sdefect(I, m) is eventually quasi-polynomial as a function in m. We compute the symbolic defect explicitly for certain monomial ideals arising from graphs, termed cover ideals. We go on to give a formula for the Waldschmidt constant, an asymptotic invariant measuring the growth of the degrees of generators of symbolic powers, for ideals whose symbolic Rees algebra is Noetherian. (C) 2019 Elsevier B.V. All rights reserved.