Sectional genera of parameter ideals

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 ${\mathrm{g}}_s(Q;M)=\operatorname{hdeg}_Q(M)-{\mathrm{e}}_Q^0(M)-{\mathrm{T}}_Q^1(M)$, 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 $Q$.

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