Sectional genera of parameter ideals

Abstract

Let $M$ be a finitely generated module over a Noetherian local ring. This paper reports, for a given parameter ideal $Q$ for $M$, a criterion for the equality ${\mathrm{g}}_s(Q;M)={\mathrm{hdeg}}_Q(M)-{\mathrm{e}}_Q^0(M)-{\mathrm{T}}_Q^1(M)$, where ${\mathrm{g}}_s(Q;M)$, ${\mathrm{e}}_Q^0(M)$, ${\mathrm{e}}_Q^1(M)$, and ${\mathrm{T}}_Q^1(M)$ respectively denote the sectional genus, the multiplicity, the first Hilbert coefficient, and the Homological torsion of $M$ with respect to $Q$.

17 pages. arXiv admin note: substantial text overlap with arXiv:1404.2455

References in corpus (1)

• The first Euler characteristics versus the homological degrees

Cited by in corpus (1)

• The second Hilbert coefficients and the homological torsions of parameters