One-dimensional local rings with reduced associated graded ring and their Hilbert functions |
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Authors: | Ferruccio Orecchia |
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Affiliation: | (1) Istituto di Matematica dell'Università di Genova, Via L. B. Alberti, 4-16132 Genova, Italy |
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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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