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 On a nonvanishing of plurigenus of a threefold of general type Commun. Korean Math. Soc. 2010 Vol. 25, No. 2, 161-165 https://doi.org/10.4134/CKMS.2010.25.2.161Published online June 1, 2010 Dong-Khan Shin Konkuk University Abstract : Even though there is a formula for $h^0(X,{\mathcal O}_X(nK_X))$ for a canonical threefold $X$, it is not easy to compute $h^0(X,{\mathcal O}_X(nK_X))$ because the formula has a term due to singularities. In this paper, we find a way to control the term due to singularities. We show nonvanishing of plurigenus for the case when the index $r$ in the singularity type $\frac{1}{r}(1,-1,b)$ is sufficiently large. Keywords : pluricanonical system, plurigenus, threefold of general type MSC numbers : 14E05, 14J99 Downloads: Full-text PDF