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- W2025209298 abstract "The set of Hilbert functions of standard graded algebras is considered as a partially ordered set under numerical comparison. For the set of algebras H(d, e0), of a given dimension d and multiplicity e0, we describe the requirements its maximal elements must satisfy; under fairly general conditions, the extremal functions arise from Cohen-Macaulay algebras. We also examine the subset H(d, e0, e1), of those functions whose first two coefficients of their Hilbert polynomials are assigned. Finally, we show how these results and the use of certain extended multiplicities can be used to prove finiteness theorems for the number of corresponding functions." @default.
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- W2025209298 date "2001-03-01" @default.
- W2025209298 modified "2023-09-27" @default.
- W2025209298 title "Maximal Hilbert Functions" @default.
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- W2025209298 doi "https://doi.org/10.1007/bf03322678" @default.
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