The Hilbert Coefficients of the Fiber Cone and the a-Invariant of the Associated Graded Ring

D'Cruz, Clare ; Puthenpurakal, Tony J.

Canadian journal of mathematics, Tome 61 (2009) no. 4, pp. 762-778

Résumé

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.

Détail

DOI : 10.4153/CJM-2009-041-1

Mots-clés : 13A30, 13D40, fiber cone, a-invariant, Hilbert coefficients of fiber cone

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