The second Hilbert coefficients and the homological torsions of parameters

Shiro Goto; Kazuho Ozeki

The second Hilbert coefficients and the homological torsions of parameters

Commutative Algebra 2014-05-20 v1

Authors: Shiro Goto , Kazuho Ozeki

Abstract

Let $M$ be a finitely generated module over a Noetherian local ring. This paper gives, for a given parameter ideal $Q$ for $M$ , bounds for the second Hilbert coefficients ${\mathrm{e}}_Q^2(M)$ in terms of the homological degrees and torsions of modules. We also report a criterion for a certain equality of the second Hilbert coefficients of parameters and the homological torsions of modules.

Keywords

Hilbert coefficients homological torsions parameter ideals Noetherian local rings finitely generated modules homological degrees

Cite

@article{arxiv.1405.4798,
  title  = {The second Hilbert coefficients and the homological torsions of parameters},
  author = {Shiro Goto and Kazuho Ozeki},
  journal= {arXiv preprint arXiv:1405.4798},
  year   = {2014}
}

Comments

20 pages. arXiv admin note: substantial text overlap with arXiv:1404.2455, arXiv:1404.4680

The second Hilbert coefficients and the homological torsions of parameters

Abstract

Keywords

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