ON A NONVANISHING OF PLURIGENUS OF A THREEFOLD OF GENERAL TYPE

Title & Authors
ON A NONVANISHING OF PLURIGENUS OF A THREEFOLD OF GENERAL TYPE
Shin, Dong-Khan;

Abstract
Even though there is a formula for $\small{h^0}$(X, $\small{\cal{O}_X(nK_X)}$) for a canonical threefold X, it is not easy to compute $\small{h^0}$(X, $\small{\cal{O}_X(nK_X)}$) 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 $\small{\frac{1}{r}}$(1, -1, b) is sufficiently large.
Keywords
pluricanonical system;plurigenus;threefold of general type;
Language
English
Cited by
References
1.
A. R. Fletcher, Contributions to Riemann-Roch on projective 3-folds with only canonical singularities and applications, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 221-231, Proc. Sympos. Pure Math., 46, Part 1, Amer. Math. Soc., Providence, RI, 1987.

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.