On the Q-divisor method and its application

Abstract

For smooth projective 3-folds of general type, we prove that the relative canonical stability ${\mu }_s(3)\le 8$. This is induced from our improved result of Kollár: the m-canonical map of a smooth projective 3-fold of general type is birational whenever $m\ge 5k+6$, provided $P_k(X)\ge 2$. The Q-divisor method is intensively developed to prove our results.

14 pages, ALatex, the final version, accepted for publication by Journal of Pure and Applied Algebra