On Fiber Coefficients 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 depth G(I) ≥ d − 1, depth FK(I) ≥ d − 2, and r(I|K) < ∞, we calculate the fiber coefficients fi(I). Under the above assumptions on depth G(I) and r(I|K), we give an upper bound for f1(I), and also provide a characterization, in terms of f1(I), of the condition depth FK(I) ≥ d − 2.