Fiber Coefficients and Depth of Fiber Cones

Abstract

Let (R, 𝔪) be a Cohen–Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R, and K an ideal containing I. When r(I | K)<∞, we give a lower bound and an upper bound for f 1(I). Under the above assumption on r(I | K) and depth G(I) ≥ d − 1, we also provide a characterization, in terms of f 1(I), of the condition depth F K (I) ≥ d − 1.