{"paper":{"title":"Some constraints on positive entropy automorphisms of smooth threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"John Lesieutre","submitted_at":"2015-03-26T19:21:42Z","abstract_excerpt":"Suppose that $X$ is a smooth, projective threefold over $\\mathbb C$ and that $\\phi : X \\to X$ 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. In explaining why th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07834","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}