The second Hilbert coefficients and the homological torsions of parameters

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.

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

References in corpus (2)

• Sectional genera of parameter ideals
• The first Euler characteristics versus the homological degrees