Ratliff-Rush filtration, regularity and depth of higher associated graded modules. Part II

Let (A, m) be a Noetherian local ring, let M be a finitely generated Cohen-Macaulay A-module of dimension r >= 2 and let I be an ideal of definition for M. Set L-I(M) = circle plus(n >= 0) M/In+1 M. In part one of this paper we showed that L-I(M) is a module over R(I), the Rees algebra of I and we gave many applications of L-I(M) to study the associated graded module, G(I)(M). In this paper we give many further applications of our technique; most notable is a complete characterization of good behavior of the Ratliff-Rush filtration modulo a superficial element. (C) 2016 Published by Elsevier B.V