On the degree of the canonical maps of 3-folds

Abstract

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 $m$.