{"paper":{"title":"Plane model-fields of definition, fields of definition, the field of moduli of smooth plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Eslam Badr, Francesc Bars","submitted_at":"2017-05-02T10:50:01Z","abstract_excerpt":"Given a smooth plane curve $\\overline{C}$ of genus $g\\geq 3$ over an algebraically closed field $\\overline{k}$, a field $L\\subseteq\\overline{k}$ is said to be a \\emph{plane model-field of definition for $\\overline{C}$} if $L$ is a field of definition for $\\overline{C}$, i.e. $\\exists$ a smooth curve $C'$ defined over $L$ where $C'\\times_L\\overline{k}\\cong \\overline{C}$, and such that $C'$ is $L$-isomorphic to a non-singular plane model $F(X,Y,Z)=0$ in $\\mathbb{P}^2_{L}$.\n  {In this short note, we construct a smooth plane curve $\\overline{C}$ over $\\overline{\\mathbb{Q}}$, such that the field of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00901","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"}