Suppose that X is a smooth, projective threefold over C and that Φ W X ! X is an automorphism of positive entropy. We show that one of the following must hold, after replacing Φ by an iterate: I) the canonical class of X is numerically trivial; ii) Φ is imprimitive; iii) Φ 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. In explaining why the method does not apply to threefolds with terminal singularities, we exhibit a non-uniruled, terminal threefold X with in nitely many KX-negative extremal rays on NE.X/.
|Original language||English (US)|
|Number of pages||41|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - Nov 2018|
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