Suppose that X is a smooth, projective threefold over C and that phi : X -> X is an automorphism of positive entropy. We show that one of the following must hold, after replacing phi by an iterate: i) the canonical class of X is numerically trivial; ii) phi is imprimitive; iii) phi is not dynamically minimal. As a consequence, we show that if a smooth threefold M does not admit a primitive automorphism of positive entropy, then no variety constructed by a sequence of smooth blow-ups of M can admit a primitive automorphism of positive entropy.
展开▼
