Generalized Hilbert coefficients and the S(2)-ification of a Rees algebra

Let A be a local ring with maximal ideal m. For an arbitrary ideal I of A, we define new invariants that generalize the classical Hilbert coefficients associated to an m-primary ideal. Using these new invariants we give a numerical characterization of the homogeneous components of the S2-ification of the extended Rees algebra S = A[It, t -1].