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

Abstract

The conjecture of Wolmer Vasconcelos on the vanishing of the first Hilbert coefficient e1(Q) is solved affirmatively, where Q is a parameter ideal in a Noetherian local ring. Basic properties of the rings for which e1(Q) vanishes are derived. The invariance of e1(Q) for parameter ideals Q and its relationship to Buchsbaum rings are studied.

Cite this paper

@inproceedings{Ghezzi2010CohenMacaulaynessVT, title={Cohen–Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals}, author={Luca Luigi Ghezzi and Shiro Goto and J. Hong and Kazuho Ozeki and Thien Thuong Phuong and Wolmer V. Vasconcelos}, year={2010} }