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

Abstract

Let A be a local ring with maximal ideal m . For an arbitrary ideal I of A, we define the generalized Hilbert coefficients j k(I)∈ Z k+1 (0⩽k⩽ dim A) . When the ideal I is m -primary, j k ( I)=(0,…,0,(−1) k e k ( I)), where e k ( I) is the classical kth Hilbert coefficient of I. Using these coefficients we give a numerical characterization of the homogeneous components of the S 2-ification of S= A[ It, t −1], extending previous results obtained by the author to not necessarily m -primary ideals.