{"paper":{"title":"The decomposition groups of plane conics and plane rational cubics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Isac Hed\\'en, Susanna Zimmermann, Tom Ducat","submitted_at":"2017-06-08T12:10:50Z","abstract_excerpt":"The decomposition group of an irreducible plane curve $X\\subset\\mathbb P^2$ is the subgroup $\\mathrm{Dec}(X)\\subset\\mathrm{Bir}(\\mathbb P^2)$ of birational maps which restrict to a birational map of $X$. We show that $\\mathrm{Dec}(X)$ is generated by its elements of degree $\\leq2$ when $X$ is either a conic or rational cubic curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02533","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"}