Dual Hilbert coefficient and width of the dual fiber cone relative to an Artinian module
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Let $(R,\mm)$ be a quasi-local ring and $M$ be a co-Cohen-\linebreak Macaulay Artinian $R$-module with $\Ndim M = d > 0$. Suppose $I$ is an ideal of $R$ such that $\lambda(0:_M I) < \infty$. In this paper, we establish formulas for the first dual Hilbert coefficient $g'_1(I,M)$, a dual form of \cite[Theorem 4.3 and 5.3]{JV}, under the assumption the width of the dual fiber cone ${\mathcal{F}'}(I,M)$ is at least $d-1$.
Abstract
Let $(R,\mm)$ be a quasi-local ring and $M$ be a co-Cohen-\linebreak Macaulay Artinian $R$-module with $\Ndim M = d > 0$. Suppose $I$ is an ideal of $R$ such that $\lambda(0:_M I) < \infty$. In this paper, we establish formulas for the first dual Hilbert coefficient $g'_1(I,M)$, a dual form of \cite[Theorem 4.3 and 5.3]{JV}, under the assumption the width of the dual fiber cone ${\mathcal{F}'}(I,M)$ is at least $d-1$.