Variation of Hilbert coefficients

Abstract. For a Noetherian local ring (R,m), the first two Hilbert coeffi-cients, e0 and e1, of the I-adic filtration of an m-primary ideal I are known to code for properties of R, of the blowup of Spec(R) along V (I), and even of their normalizations. We give estimations for these coefficients when I is enlarged (in the case of e1 in the same integral closure class) for general Noe-therian local rings. 1