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

Published online by Cambridge University Press:  20 November 2018

Clare D'Cruz  and
Tony J. Puthenpurakal
Clare D'Cruz
Affiliation:
Chennai Mathematical Institute, Plot H1, SIPCOT IT Park Padur PO, Siruseri 603103, India, e-mail: [email protected]
Tony J. Puthenpurakal
Affiliation:
Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India, e-mail: [email protected]
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Abstract

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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.

Keywords

13A3013D40fiber conea-invariantHilbert coefficients of fiber cone
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 4 , 01 August 2009 , pp. 762 - 778
Copyright
Copyright © Canadian Mathematical Society 2012

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