Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2010; 25(2): 161-165

Printed June 1, 2010

https://doi.org/10.4134/CKMS.2010.25.2.161

Copyright © The Korean Mathematical Society.

On a nonvanishing of plurigenus of a threefold of general type

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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