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

Clare D'Cruz; Tony J. Puthenpurakal

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arXiv · math/0601510

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

Clare D'Cruz·Tony J. Puthenpurakal

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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.

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Clare D'Cruz, Tony J. Puthenpurakal. 2007-04-21. The Hilbert Coefficients of the fiber cone and the $a$-invariant of the associated graded ring. https://arxiv.org/abs/math/0601510

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