ABSTRACT
For a regular ideal I having a principal reduction in a Noetherian local ring (R, m) we consider properties of the powers of I as reflected in the fiber cone F (I) and the associated graded ring G (I) of I. In particular, we examine the postulation number of F (I) and compare it with the reduction number of I, and the postulation number of G (I) when the latter is meaningful. We discuss a sufficient condition for F (I) to be Cohen‐Macaulay and consider for a fixed R what is possible for the reduction number r (I) of I and the multiplicity of F (I).
