The Hilbert Coefficients of the fiber cone and the $a$-invariant of the associated graded ring
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Let $(A,\m)$ be a Noetherian local ring with infinite residue field and let $I$ be an ideal in $A$ and let $F(I) = \oplus_{n \geq 0}I^n/\m I^n$ be the fiber-cone of $I$. We prove certain relations among the Hilbert coefficients of $F(I)$ when the $a$-invariant of the associated graded ring $G(I)$ is negative.
To appear in Canadian Journal of Math. Many examples added in section 5 on analytic spread three. Introduction is longer and more describtive. An appendix on filter regular sequences and minimal reductions added
To appear in Canadian Journal of Math. Many examples added in section 5 on analytic spread three. Introduction is longer and more describtive. An appendix on filter regular sequences and minimal reductions added