Hilbert coefficients and the Gorenstein property of the associated graded ring

摘要

In this article we investigate the Gorenstein property of the associated graded ring G(A)(I) of an ideal I in a Gorenstein local ring (A, m) of positive dimension. We especially concentrate on the case where I is m-primary. Assuming that the Rees algebra of I is Cohen-Macaulay we then give necessary and sufficient conditions for the Gorensteiness of G(A)(I) in terms of the Hilbert coefficients of I. (C) 2004 Elsevier Inc. All rights reserved. [References: 26]