Necessary and sufficient conditions for the Cohen-Macaulayness of form rings (Q1284095)

Huckaba and Huneke studied the Cohen-Macaulayness of the graded ring associated to an ideal \(I\) of a Cohen-Macaulay local ring \(A\) under the assumption that \(\text{depth}(A/I^n)\) is big enough [cf. \textit{S. Huckaba} and \textit{C. Huneke}, Am. J. Math. Soc. 114, No. 2, 367-403 (1992; Zbl 0758.13001)]. The question was studied also by others authors (see the references in the paper under review). The purpose of this paper is to give a necessary and sufficient condition for this property, in the same assumptions. One shows also how the depth of the graded ring is related to the vanishing of components of the graded local cohomology.