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1. CJM 2009 (vol 61 pp. 762)
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The Hilbert Coefficients of the Fiber Cone and the $a$-Invariant of the Associated Graded Ring Let $(A,\m)$ be a Noetherian local ring with infinite residue
field and let $I$ be an ideal in $A$ and let $F(I) =
\bigoplus_{n \geq 0}I^n/\m I^n$ 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.
Keywords:fiber cone, $a$-invariant, Hilbert coefficients of fiber cone Categories:13A30, 13D40 |