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An Upper Bound for the First Hilbert Coefficient of Gorenstein Algebras and Modules

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 نشر من قبل Hema Srinivasan
 تاريخ النشر 2020
  مجال البحث
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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.



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