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 nby 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.
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Sally, J.D. (1994). Rigid Hilbert Polynomials for m-Primary Ideals. In: Bajaj, C.L. (eds) Algebraic Geometry and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2628-4_23
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DOI: https://doi.org/10.1007/978-1-4612-2628-4_23
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