The relative pluricanonical stability for 3-folds of general type

Details The relative pluricanonical stability for 3-folds of general type The relative pluricanonical stability for 3-folds of general type

1999-02-06

arxiv.org/abs/math/9902047v3

Proc. Amer. Math. Soc. 129(2001), no.7, 1927-1937

Mathematics

Algebraic Geometry

11 pages, new version, Amstex, to appear in Proceedings AMS

Scientific paper

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.

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