Bounds for hilbert coefficients

Abstract

Let (A, m) be a noetherian local ring and J an m-primary ideal. Elias [3] proved that depth(G(Jk)) is constant for k >> 0 and denoted this number by σ(J). In this paper, we prove the non-positivity for the Hilbert coefficients ei(J) under some conditions for σ(J). In case of J = Q is a parameter ideal, we establish bounds for the Hilbert coefficients of Q in terms of the dimension and the first Hilbert coefficient e1(Q).