On the Q-divisor method and its application

Details On the Q-divisor method and its application On the Q-divisor method and its application

1999-04-02

arxiv.org/abs/math/9904005v5

Mathematics

Algebraic Geometry

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

Scientific paper

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

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