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

L. Ghezzi; S. Goto; J. Hong; K. Ozeki; T. T. Phuong; W. V. Vasconcelos

doi:10.1112/jlms/jdq008

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

Commutative Algebra 2014-02-26 v1

Authors: L. Ghezzi , S. Goto , J. Hong , K. Ozeki , T. T. Phuong , W. V. Vasconcelos

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

Cohen-Macaulayness first Hilbert coefficient parameter ideal Noetherian local ring Buchsbaum ring

Cite

@article{arxiv.1002.0391,
  title  = {Cohen--Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals},
  author = {L. Ghezzi and S. Goto and J. Hong and K. Ozeki and T. T. Phuong and W. V. Vasconcelos},
  journal= {arXiv preprint arXiv:1002.0391},
  year   = {2014}
}

Comments

To appear in the Journal of the London Mathematical Society

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

Abstract

Keywords

Cite

Comments

Related papers