摘要
Let （R,m） be a Cohen-Macaulay local ring of dimension d with infinite residue field, I an m-primary ideal and K an ideal containing I. Let J be a minimal reduction of I such that, for some positive integer k, KIn ∩ J = JKIn-1 for n ≤ k ？ 1 and λ（ JKKIIkk-1 ） = 1. We show that if depth G（I） ≥ d-2, then such fiber cones have almost maximal depth. We also compute, in this case, the Hilbert series of FK（I） assuming that depth G（I） ≥ d - 1.
Let （R,m） be a Cohen-Macaulay local ring of dimension d with infinite residue field, I an m-primary ideal and K an ideal containing I. Let J be a minimal reduction of I such that, for some positive integer k, KIn ∩ J = JKIn-1 for n ≤ k ？ 1 and λ（ JKKIIkk-1 ） = 1. We show that if depth G（I） ≥ d-2, then such fiber cones have almost maximal depth. We also compute, in this case, the Hilbert series of FK（I） assuming that depth G（I） ≥ d - 1.
基金
Supported by the National Natural Science Foundation of China (Grant No.10771152)
