The relative pluricanonical stability for 3-folds of general type
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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 $p_{g}(X)\ge 3$.References
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Additional Information
- Meng Chen
- Affiliation: Department of Applied Mathematics, Tongji University, Shanghai, 200092, People’s Republic of China
- Email: mchen@mail.tongji.edu.cn
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1927-1937
- MSC (1991): Primary 14C20, 14E05, 14E35
- DOI: https://doi.org/10.1090/S0002-9939-00-05870-6
- MathSciNet review: 1825899