The reduction number of canonical ideals

Graded filtrations and ideals of reduction number 2

“…$$\mathrm{e}_0(I), \mathrm{e}_1(I), \dots , \mathrm{e}_{d}(I)$$ are called the Hilbert coefficients of I . The problem to reveal the relation between the Hilbert coefficients of I and the structures of $$\mathcal {R}(I)$$ and $$\mathcal {G}(I)$$ is studied very much by many researchers (see papers [3–5, 7, 9–12, 16–18, 20, 22, 23] or a book [19]). One of the most famous results in this direction is the following obtained by Northcott, Huneke, and Ooishi.…”