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Rigid Hilbert Polynomials for m-Primary Ideals

In: Algebraic Geometry and its Applications

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  • Judith D. Sally

Abstract

Which Hilbert polynomials for an m-primary ideal I in a d-dimensional, (d > 0), local Cohen-Macaulay ring (R, m) determine Heilbert function of I? For example, if we denote the Hilbert function giving the length of R/I n by H I (n) and the corresponding polynomial by p I (X), then any m -primary ideal I having Hilbert polynomial $$p_I(X) = \lambda \left( {X + \mathop d\limits_d - 1} \right)$$ , has Hilbert function $$H_I = \lambda \left( {n + \mathop d\limits_d - 1} \right)$$ for all n > 0 and, in addition, I must be generated by d elements.

Suggested Citation

  • Judith D. Sally, 1994. "Rigid Hilbert Polynomials for m-Primary Ideals," Springer Books, in: Chandrajit L. Bajaj (ed.), Algebraic Geometry and its Applications, chapter 23, pages 375-379, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2628-4_23
    DOI: 10.1007/978-1-4612-2628-4_23
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