{"paper":{"title":"Hypersurface model-fields of definition for smooth hypersurfaces and their twists","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":"2018-04-17T09:09:14Z","abstract_excerpt":"Given a smooth projective variety of dimension $n-1\\geq 1$ defined over a perfect field $k$ that admits a non-singular hypersurface modelin $\\mathbb{P}^n_{\\overline{k}}$ over $\\overline{k}$, a fixed algebraic closure of $k$, it does not necessarily have a non-singular hypersurface model defined over the base field $k$. We first show an example of such phenomenon: a variety defined over $k$ admitting non-singular hypersurface models but none defined over $k$. We also determine under which conditions a non-singular hypersurface model over $k$ may exist. Now, even assuming that such a smooth hype"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06118","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"}