具有几乎最大深度的滤链的Hilbert 系数

Hilbert Coefficients of Filtrations with Almost Maximal Depth

中文关键词:  Hilbert系数  纤维锥  深度.

英文关键词:Hilbert coefficients  fiber cones  depth.

中文摘要:

      设${\cal F}$是Cohen-Macaulay R-模的一个Hilbert滤链. 当$G({\cal F},M)$和$F_K({\cal F},M)$有几乎最大深度时,我们证明长度$\lambda(KI_nM/JI_{n-1}M)$和约化数$r^K_J({\cal F},M)$与$J$无关,并且给出了第一和第二个Hilbert 系数的下界.

英文摘要:

      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.