On a nonvanishing of plurigenus of a threefold of general type
Commun. Korean Math. Soc. 2010 Vol. 25, No. 2, 161-165
Published 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
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