Abstract:
I am going to explain the proof of the Lesieutre's Theorem classifying smooth threefolds with a structure of a regular automorphism with positive entropy. By this theorem either the canonical class of such a threefold is numerically trivial, or the automorphism is not primitive, i.e. it preserves a structure of a rational map to a variety of smaller dimension, or the automorphism extends to a regular automorphism of a blow-down of a divisor in the threefold. In particular, this implies that any automorphism with positive entropy on a sequence of blow-ups with smooth centers of a projective space is imprimitive.