{"paper":{"title":"Automorphism groups of origami curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ruben A. Hidalgo","submitted_at":"2019-07-24T20:01:31Z","abstract_excerpt":"A closed Riemann surface $S$ (of genus at least one) is called an origami curve if it admits a non-constant holomorphic map $\\beta:S \\to E$ with at most one branch value, where $E$ is a genus one Riemann surface. In this case, $(S,\\beta)$ is called an origami pair and ${\\rm Aut}(S,\\beta)$ is the group of conformal automorphisms $\\phi$ of $S$ such that $\\beta=\\beta \\circ \\phi$. Let $G$ be a finite group. It is a known fact that $G$ can be realized as a subgroup of ${\\rm Aut}(S,\\beta)$ for a suitable origami pair $(S,\\beta)$. It is also known that $G$ can be realized as a group of conformal auto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10692","kind":"arxiv","version":1},"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"}