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The Hilbert Coefficients of the Fiber Cone and the a-Invariant of the Associated Graded Ring
Published online by Cambridge University Press: 20 November 2018
Abstract
Let $(A,\mathfrak{m})$ be a Noetherian local ring with infinite residue field and let
$I$ be an ideal in
$A$ and let
$F(I)={{\oplus }_{n\ge 0}}{{I}^{n}}/\mathfrak{m}{{I}^{n}}$ be the fiber cone of
$I$. We prove certain relations among the Hilbert coefficients
${{f}_{0\,}}(I),\,{{f}_{1}}(I),\,{{f}_{2}}(I)$ of
$F(I)$ when the
$a$-invariant of the associated graded ring
$G(I)$ is negative.
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- Research Article
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- Copyright © Canadian Mathematical Society 2012
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