The relative pluricanonical stability for 3-folds of general type
Abstract
This paper aims to improve a theorem of Janos Kollar. For a given Complex projective threefold X of general type, suppose the plurigenus pk(X) 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 13k+6. If Pk(X) 3, then the m-canonical map is stably birational for m 10k+8. In particular, the 12-canonical map is birational when pg(X) 2 and the 11-canonical map is birational when pg(X) 3.
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