## The generic finiteness of the $$m$$-canonical map for 3-folds of general type.(English)Zbl 1092.14049

Let $$X$$ be a projective minimal 3-fold of general type with only $$\mathbb{Q}$$-factorial terminal singularities. The author shows that if $$P_g(X)\geq 5$$, then the $$3$$-canonical map is generically finite and if $$P_g(X)\geq 2$$ and $$q(X)\geq 3$$ then the $$m$$-canonical map is generically finite for $$m\geq 3$$.

### MSC:

 14J30 $$3$$-folds 14E05 Rational and birational maps

### Keywords:

3-folds; pluricanonical maps