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One-dimensional local rings with reduced associated graded ring and their Hilbert functions

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Abstract

Let A be a one-dimensional reduced local ring with finite normalization. Let G(A) be the associated graded ring of A. In this paper we analyse the two conditions: Proj (G(A)) reduced and G(A) reduced together with their relations with the equality H(n)=HR (n), where H(n) and HR (n) are respectively the Hilbert function of the ring A and of the local ring R of G(A)red=G(A)/nil (G(A)) at its homogenous maximal ideal. As a consequence of our results we get a class of ordinary singularities with H(n) locally decreasing for any embedding dimension H(1) greater then 4.

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  1. Istituto di Matematica dell'Università di Genova, Via L. B. Alberti, 4-16132, Genova, Italy

    Ferruccio Orecchia

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  1. Ferruccio Orecchia
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Orecchia, F. One-dimensional local rings with reduced associated graded ring and their Hilbert functions. Manuscripta Math 32, 391–405 (1980). https://doi.org/10.1007/BF01299612

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  • DOI: https://doi.org/10.1007/BF01299612

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