Canonical stability in terms of singularity index for algebraic threefolds
Algebraic Geometry
2009-10-31 v2
Abstract
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)
Keywords
Cite
@article{arxiv.math/0004076,
title = {Canonical stability in terms of singularity index for algebraic threefolds},
author = {Meng Chen},
journal= {arXiv preprint arXiv:math/0004076},
year = {2009}
}
Comments
27 pages, The final version, Accepted for publication in Math. Proc. Camb. Phil. Soc