Hilbert coefficients and the Gorenstein property of the associated graded ring

In this article we investigate the Gorenstein property of the associated graded ring GA(I) of an ideal I in a Gorenstein local ring of positive dimension. We especially concentrate on the case where I is -primary. Assuming that the Rees algebra of I is Cohen–Macaulay we then give necessary and sufficient conditions for the Gorensteiness of GA(I) in terms of the Hilbert coefficients of I.