A numerical characterization of the S2-ification of a Rees algebra

Let A be a local ring with maximal ideal image. For an arbitrary ideal I of A, we define the generalized Hilbert coefficients image (0less-than-or-equals, slantkless-than-or-equals, slantdim A). When the ideal I is image-primary, jk(I)=(0,…,0,(−1)kek(I)), where ek(I) is the classical kth Hilbert coefficient of I. Using these coefficients we give a numerical characterization of the homogeneous components of the S2-ification of S=A[It,t−1], extending previous results obtained by the author to not necessarily image-primary ideals.