Hilbert Coefficients of Filtrations with Almost Maximal Depth

Abstract:

      Let ${\cal F}$ be a Hilbert filtration with respect to a Cohen-Macaulay $R$-module $M$. When $G({\cal F},M)$ and $F_K({\cal F},M)$ have almost maximal depths, we show that the length $\lambda(KI_{n}M/KJI_{n-1}M)$ and the reduction number $r_{J}^{K}({\cal F},M)$ are independent of $J$. Lower bounds for the first and second Hilbert coefficients are obtained.