Cohen--Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals
arXiv:1002.0391 · doi:10.1112/jlms/jdq008
Abstract
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.
To appear in the Journal of the London Mathematical Society