Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the degree of the canonical maps of 3-folds

Christopher Derek Hacon

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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 $\phi\colon X \dashrightarrow \mathbf{P}^{p_g-1}$, then $\deg(\phi) \leq 576$. For any positive integer $m > 0$, we give infinitely many examples of (non-Gorenstein) 3-folds of general type with canonical map of degree $m$.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 80, Number 8 (2004), 166-167.

First available in Project Euclid: 18 May 2005

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Zentralblatt MATH identifier

Primary: 14J30: $3$-folds [See also 32Q25] 14E35

Canonical maps threefolds


Hacon, Christopher Derek. On the degree of the canonical maps of 3-folds. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 8, 166--167. doi:10.3792/pjaa.80.166.

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