Bulletin of the
Korean Mathematical Society BKMS

For a canonical threefold $X$, it is known that $p_n$ does not vanish for a sufficiently large $n$, where $p_n=h^0(X,{\mathcal O}_X(nK_X))$. We have shown that $p_n$ does not vanish for at least one $n$ in $\{6,\,8,\,10\}$. Assuming an additional condition $p_2\geq 1$ or $p_3\geq 1$, we have shown that $p_{12}\geq 2$ and $p_n\geq 2$ for $n\geq 14$ with one possible exceptional case. We have also found some inequalities between $\chi({\mathcal O}_X)$ and $K_X^3$.

Keywords: canonical threefold, threefold of general type, plurigenus

MSC numbers: 14J17, 14J30