{"paper":{"title":"Finiteness theorems on hypersurfaces in partial differential-algebraic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.LO","authors_text":"James Freitag, Rahim Moosa","submitted_at":"2016-06-27T21:26:48Z","abstract_excerpt":"Hrushovski's generalization and application of [Jouanolou, \"Hypersurfaces solutions d'une \\'equation de Pfaff analytique\", Mathematische Annalen, 232 (3):239--245, 1978] is here refined and extended to the partial differential setting with possibly nonconstant coefficient fields. In particular, it is shown that if $X$ is a differential-algebraic variety over a partial differential field F that is finitely generated over its constant field F_0, then there exists a dominant differential-rational map from X to the constant points of an algebraic variety V over F_0, such that all but finitely many"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08492","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"}