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

Laura Ghezzi, Shiro Goto, J. Hong, Kazuho Ozeki, Tran Thi Phuong, Wolmer V. Vasconcelos

• 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.