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The relative pluricanonical stability for 3-folds of general type

Author: Meng Chen
Journal: Proc. Amer. Math. Soc. 129 (2001), 1927-1937
MSC (1991): Primary 14C20, 14E05, 14E35
Published electronically: November 22, 2000
MathSciNet review: 1825899
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Abstract: The aim of this paper is to improve a theorem of János Kollár by a different method. For a given smooth complex projective threefold $X$ of general type, suppose the plurigenus $P_{k}(X)\ge 2$. Kollár proved that the $(11k+5)$-canonical map is birational. Here we show that either the $(7k+3)$-canonical map or the $(7k+5)$-canonical map is birational and that the $(13k+6)$-canonical map is stably birational onto its image. Suppose $P_{k}(X)\ge 3$. Then the $m$-canonical map is birational for $m\ge 10k+8$. In particular, $\phi_{12}$ is birational whenever $p_{g}(X)\ge 2$ and $\phi_{11}$ is birational whenever $p_{g}(X)\ge 3$.

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Additional Information

Meng Chen
Affiliation: Department of Applied Mathematics, Tongji University, Shanghai, 200092, People’s Republic of China

Received by editor(s): December 12, 1998
Received by editor(s) in revised form: November 12, 1999
Published electronically: November 22, 2000
Additional Notes: The author was supported in part by the National Natural Science Foundation of China
Communicated by: Ron Donagi
Article copyright: © Copyright 2000 American Mathematical Society

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