The second Hilbert coefficients and the sectional genera of ideals

Abstract

This paper gives an upper bound of the second Hilbert coefficients ${\mathrm{e}}_2(I)$ of $\mathfrak{m}$-primary ideals $I$ in a Cohen-Macaulay local ring $(A,\mathfrak{m})$ in terms of the sectional genera of $I$.

13 pages