Some constraints on positive entropy automorphisms of smooth threefolds

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Abstract

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 languageEnglish (US)
Pages (from-to)1507-1547
Number of pages41
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume6
Issue number51
DOIs
StatePublished - Nov 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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