{"paper":{"title":"On automorphisms of blowups of $\\mathbb{P}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DS","authors_text":"Tuyen Trung Truong","submitted_at":"2012-02-20T05:07:21Z","abstract_excerpt":"Let $\\pi :X\\rightarrow \\mathbb{P}^3$ be a finite composition of blowups along smooth centers. We show that for \"almost all\" of such $X$, if $f\\in Aut(X)$ then its first and second dynamical degrees are the same. We also construct many examples of finite blowups $X\\rightarrow \\mathbb{P}^3$, whose automorphism group $Aut(X)$ has only finitely many connected components.\n  We also present a heuristic argument showing that for a \"generic\" compact K\\\"ahler manifold $X$ of dimension $\\geq 3$, the automorphism group $Aut(X)$ has only finitely many connected components."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4224","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"}