Canonical stability in terms of singularity index for algebraic threefolds

Details Canonical stability in terms of singularity index for algebraic threefolds Canonical stability in terms of singularity index for algebraic threefolds

2000-04-12

arxiv.org/abs/math/0004076v2

Math. Proc. Cambridge Philos. Soc. 131(2001), no.2, 241-264

Mathematics

Algebraic Geometry

27 pages, The final version, Accepted for publication in Math. Proc. Camb. Phil. Soc

Scientific paper

10.1017/S030500410100531X

Let X be a projective 3-fold with at most Q-factorial terminal singularities on which K_X is nef and big. Suppose the canonical index r(X)>1. For any positive integer m, it is interesting to consider the base point freeness and birationality of the divisor mK_X. For example, we know the following results: (1) the system |5rK_X| is base point free (Ein-Lazarsfeld-Lee); (2) |mK_X| gives a birational map for all m>4r+2 (M. Hanamura). This article aims to present a better result in direction (2). As far as our method can tell here, |mK_X| gives a birational map for all m>2r+5. (Q-divisor method + patient calculation)

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