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).
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