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On the $$\mathbb Q$$-divisor method and its application. (English) Zbl 1049.14034
Summary: For a smooth projective 3-fold of general type, we prove that the relative canonical stability $$\mu_s(3) \leqslant 8$$. This is induced by our improved result of Kollár: the $$m$$-canonical map of $$X$$ is birational onto its image whenever $$m \geqslant 5k+6$$, provided $$P_k(X) \geqslant 2$$. The $$\mathbb Q$$-divisor method is intensively developed to prove our results.

##### MSC:
 14J30 $$3$$-folds 14C20 Divisors, linear systems, invertible sheaves 14E05 Rational and birational maps
##### Keywords:
relative canonical stability
Full Text:
##### References:
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