论文标题
Gorenstein代数和模块的第一个希尔伯特系数的上限
An Upper Bound for the First Hilbert Coefficient of Gorenstein Algebras and Modules
论文作者
论文摘要
令$ r $成为一个多项式戒指，而$ m = \ bigoplus_n m_n $是有限生成的分级$ r $ module，是由零度的同质元素生成的，并分级为$ r $ r $ r $ r $ - minimal-minimal-minimal-minimal-minimal nimimal nosity $ \ mathbf {f} $。当分级分辨率对称时，Cohen-Macaulay模块$ m $是Gorenstein。就$ m $的分级分辨率的变化而言，我们为第一个希尔伯特系数（$ e_1 $）提供了上限。当$ m = r/i $，gorenstein代数时，这种界限与以准假分辨率的Gorenstein代数中\ cite {es}获得的界限一致。我们猜想了针对较高系数的类似结合。
Let $R$ be a polynomial ring over a field and $M= \bigoplus_n M_n$ a finitely generated graded $R$-module, minimally generated by homogeneous elements of degree zero with a graded $R$-minimal free resolution $\mathbf{F}$. A Cohen-Macaulay module $M$ is Gorenstein when the graded resolution is symmetric. We give an upper bound for the first Hilbert coefficient, $e_1$ in terms of the shifts in the graded resolution of $M$. When $M = R/I$, a Gorenstein algebra, this bound agrees with the bound obtained in \cite{ES} in Gorenstein algebras with quasi-pure resolution. We conjecture a similar bound for the higher coefficients.
