Hilbert coefficients and depths of form rings

Details Hilbert coefficients and depths of form rings Hilbert coefficients and depths of form rings

2002-06-21

arxiv.org/abs/math/0206221v2

Mathematics

Commutative Algebra

7 pages; This is a slightly modified version of the previously uploaded file

Scientific paper

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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