The Hilbert Coefficients of the fiber cone and the $a$-invariant of the associated graded ring

Abstract

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.

arXiv commentTo 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