Depth of associated graded rings via Hilbert coefficients of ideals

Abstract

Given a local Cohen-Macaulay ring $(R,\mathfrak{m})$, we study the interplay between the integral closedness -- or even the normality -- of an $\mathfrak{m}$-primary $R$-ideal $I$ and conditions on the Hilbert coefficients of $I$. We relate these properties to the depth of the associated graded ring of $I$.

17 pages. J. Pure and Applied Algebra, to appear