On the degree of the canonical maps of 3-folds. (English) Zbl 1068.14046

Summary: We prove the following result that answers a question of M. Chen: Let \(X\) be a Gorenstein minimal complex projective 3-fold of general type with locally factorial terminal singularities. If \(|K_X|\) defines a generically finite map \(\varphi:X \to\mathbb{P}^{p_g-1}\), then \(\deg (\varphi)\leq 576\). For any positive integer \(m>0\), we give infinitely many examples of (non-Gorenstein) 3-folds of general type with canonical map of degree \(m\).


14J30 \(3\)-folds
14E20 Coverings in algebraic geometry
14C20 Divisors, linear systems, invertible sheaves
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