# ON A NONVANISHING OF PLURIGENUS OF A THREEFOLD OF GENERAL TYPE

• Shin, Dong-Khan
• Published : 2010.04.30
• 67 6

#### 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

#### References

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2. 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.
3. D.-K. Shin, On a computation of plurigenera of a canonical threefold, J. Algebra 309 (2007), no. 2, 559-568. https://doi.org/10.1016/j.jalgebra.2006.03.034