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
