[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2010.25.2.161

ON A NONVANISHING OF PLURIGENUS OF A THREEFOLD OF GENERAL TYPE

Shin, Dong-Khan (DEPARTMENT OF MATHEMATICS KONKUK UNIVERSITY)

Publication Information

Communications of the Korean Mathematical Society / v.25, no.2, 2010 , pp. 161-165 More about this Journal

Abstract

Even though there is a formula for $h^0$ (X, $\cal{O}_X(nK_X)$ ) for a canonical threefold X, it is not easy to compute $h^0$ (X, $\cal{O}_X(nK_X)$ ) 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;

Citations & Related Records

Times Cited By SCOPUS : 0

Reference

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3	M. Reid, Young person's guide to canonical singularities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 345-414, Proc. Sympos. Pure Math., 46, Part 1, Amer. Math. Soc., Providence, RI, 1987.