Cohen--Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals

Details Cohen--Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals Cohen--Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals

2010-02-02

arxiv.org/abs/1002.0391v1

Mathematics

Commutative Algebra

To appear in the Journal of the London Mathematical Society

Scientific paper

The conjecture of Wolmer Vasconcelos on the vanishing of the first Hilbert
coefficient $e_1(Q)$ is solved affirmatively, where $Q$ is a parameter ideal in
a Noetherian local ring. Basic properties of the rings for which $e_1(Q)$
vanishes are derived. The invariance of $e_1(Q)$ for parameter ideals $Q$ and
its relationship to Buchsbaum rings are studied.

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