ON A COMPUTATION OF PLURIGENUS OF A CANONICAL THREEFOLD

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 $K^3_X$.