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The Hilbert Coefficients of the Fiber Cone and the a-Invariant of the Associated Graded Ring
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- Journal:
- Canadian Journal of Mathematics / Volume 61 / Issue 4 / 01 August 2009
- Published online by Cambridge University Press:
- 20 November 2018, pp. 762-778
- Print publication:
- 01 August 2009
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- Article
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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.
