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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
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