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Hilbert coefficients and depths of form rings

A. V. Jayanthan·Balwant Singh·J. K. Verma
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Abstract

We present short and elementary proofs of two theorems of Huckaba and Marley, while generalizing them at the same time to the case of a module. The theorems concern a characterization of the depth of the associated graded ring of a Cohen-Macaulay module, with respect to a Hilbert filtration, in terms of the Hilbert coefficient e_1. As an application, we derive bounds on the higher Hilbert coefficient e_i in terms of e_0.

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BibTeXRIS

A. V. Jayanthan, Balwant Singh, J. K. Verma. 2003-01-31. Hilbert coefficients and depths of form rings. https://arxiv.org/abs/math/0206221

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