On the Q -divisor method and its application

For a smooth projective 3-fold of general type, we prove that the relative canonical stability μs(3)⩽8. This is induced by our improved result of Kollar: the m-canonical map of X is birational onto its image whenever m⩾5k+6, provided Pk(X)⩾2. The Q-divisor method is intensively developed to prove our results.