Communications of the
Korean Mathematical Society CKMS

When $X$ is a threefold of general type, it is well known $h^0(X,\cx(nK_X))\geq 1$ for a sufficiently large $n$. When $\ex>0 $, it is not easy to obtain such an integer $n$. A. R. Fletcher showed that $h^0(X,\cx(nK_X))\geq 1$ for $n=12$ when $\ex=1$. We introduce a technique different from A. R. Fletcher's. Using this technique, we also prove the same result as he showed and have a new result.

Keywords: threefold of general type, plurigenus

MSC numbers: 14J17, 14J30