{"paper":{"title":"Connectivity of the branch locus of moduli space of rational maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ruben A. Hidalgo, Saul Quispe","submitted_at":"2015-02-10T17:34:23Z","abstract_excerpt":"Milnor proved that the moduli space ${\\rm M}_{d}$ of rational maps of degree $d \\geq 2$ has a complex orbifold structure of dimension $2(d-1)$. Let us denote by ${\\mathcal S}_{d}$ the singular locus of ${\\rm M}_{d}$ and by ${\\mathcal B}_{d}$ the branch locus, that is, the equivalence classes of rational maps with non-trivial holomorphic automorphisms. Milnor observed that we may identify ${\\rm M}_2$ with ${\\mathbb C}^2$ and, within that identification, that ${\\mathcal B}_{2}$ is a cubic curve; so ${\\mathcal B}_{2}$ is connected and ${\\mathcal S}_{2}=\\emptyset$. If $d \\geq 3$, then ${\\mathcal S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03001","kind":"arxiv","version":3},"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"}