The second Hilbert coefficients and the sectional genera of ideals
  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 $I$. 
Kazuho Ozeki
math.AC