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ISSN 1088-6826(e) ISSN 0002-9939(p)

The relative pluricanonical stability for 3-folds of general type

Author(s): Meng Chen
Journal: Proc. Amer. Math. Soc. 129 (2001), 1927-1937.
MSC (1991): Primary 14C20, 14E05, 14E35
Posted: 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 of general type, suppose the plurigenus $P_{k}(X)\ge 2$ . Kollár proved that the -canonical map is birational. Here we show that either the -canonical map or the -canonical map is birational and that the -canonical map is stably birational onto its image. Suppose $P_{k}(X)\ge 3$ . Then the -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
Email: mchen@mail.tongji.edu.cn

DOI: 10.1090/S0002-9939-00-05870-6
PII: S 0002-9939(00)05870-6
Received by editor(s): December 12, 1998
Received by editor(s) in revised form: November 12, 1999
Posted: November 22, 2000
Additional Notes: The author was supported in part by the National Natural Science Foundation of China
Communicated by: Ron Donagi
Copyright of article: Copyright 2000, American Mathematical Society

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