{"paper":{"title":"Automorphism loci for the moduli space of rational maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DS","authors_text":"Brian Stout, Nikita Miasnikov, Phillip Williams","submitted_at":"2014-08-25T03:13:13Z","abstract_excerpt":"Let $k$ be an algebraically closed field of characteristic $0$ and $\\mathcal{M}_d$ the moduli space of rational maps on $\\mathbb{P}^1$ of degree $d$ over $k$. This paper describes the automorphism loci $A\\subset \\mathrm{Rat}_d$ and $\\mathcal{A}\\subset \\mathcal{M}_d$ and the singular locus $\\mathcal{S}\\subset\\mathcal{M}_d$. In particular, we determine which groups occur as subgroups of the automorphism group of some $[\\phi]\\in\\mathcal{M}_d$ for a given $d$ and calculate the dimension of the locus. Next, we prove an analogous theorem to the Rauch-Popp-Oort characterization of singular points on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5655","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"}