{"paper":{"title":"A classification of degree $2$ semi-stable rational maps $\\mathbb{P}^2\\to\\mathbb{P}^2$ with large finite dynamical automorphism group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.AG","authors_text":"Joseph H. Silverman, Michelle Manes","submitted_at":"2016-07-19T22:17:53Z","abstract_excerpt":"Let $K$ be an algebraically closed field of characteristic $0$. In this paper we classify the $\\text{PGL}_3(K)$-conjugacy classes of semi-stable dominant degree $2$ rational maps $f:{\\mathbb P}^2_K\\dashrightarrow{\\mathbb P}^2_K$ whose automorphism group $$\\text{Aut}(f):=\\{\\phi\\in\\text{PGL}_3(K): \\phi^{-1}\\circ f\\circ\\phi=f\\}$$ is finite and of order at least $3$. In particular, we prove that $\\#\\text{Aut}(f)\\le24$ in general, that $\\#\\text{Aut}(f)\\le21$ for morphisms, and that $\\#\\text{Aut}(f)\\le6$ for all but finitely many conjugacy classes of $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05772","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"}