Cohen-Macaulay normal local domains whose associated graded rings have no depth (Q1086632)

Let (B,m) be a local ring of dimension \(d\geq 2\) and consider the tangent cone \(gr_ mB:=\oplus_{n\geq 0}m^ n/m^{n+1}.\quad It\) is well known that \(gr_ mB\) is an important object associated to (B,m). In several publications J. Sally has proved that \(gr_ mB\) is a Cohen-Macaulay ring in many important cases [cf. \textit{J. Sally}, J. Algebra 56, 168-183 (1979; Zbl 0401.13016)] and she asked if there are Cohen-Macaulay local rings (B,m) for which \(gr_ mB\) has no depth. The author answers this question by exhibiting a large class of normal Cohen-Macaulay local rings whose associated graded ring \(gr_ mB\) has no depth. It should be noted that Robbiano, Valla and Ngo Viet Trung have found other examples to this question (unpublished).