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On pluricanonical maps for threefolds of general type, II
This note mainly studies the generic finiteness of \phi_m of a complex
projective 3-fold of general type. A new result on the classification to
bicanonical pencil for Gorenstein 3-folds is attached in the last section.Comment: 16 pages, Amstex, The final version, Accepted for publication in
Osaka Journal of Mathematic
The relative pluricanonical stability for 3-folds of general type
This paper aims to improve a theorem of Janos Kollar. For a given Complex
projective threefold X of general type, suppose the plurigenus p_k(X)\ge 2,
Kollar 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 m-canonical map is stably birational for m\ge 13k+6. If P_k(X)\ge 3,
then the m-canonical map is stably birational for m\ge 10k+8. In particular,
the 12-canonical map is birational when p_g(X)\ge 2 and the 11-canonical map is
birational when p_g(X)\ge 3.Comment: 11 pages, new version, Amstex, to appear in Proceedings AM
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