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In this article we define a notion of low toric degree generalizing this condition for hypersurfaces of simplicial projective split toric varieties. This allows us to prove a particular case of the $C_1$ conjecture of Koll\\'{a}r, Lang and Manin : any smooth separably rationally connected variety that can be embedded as such a hypersurface over a $C_1"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.6945","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-25T15:45:49Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"93f64b962bf09160270e697bd8632014e0c0528ff1dd15b89cd5295765f82f53","abstract_canon_sha256":"e5c98b943be40f612ccb7ba3d661eeae9e7d8bf67fb07231461d5fb6bcb27727"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:48.878065Z","signature_b64":"9ViTZJ8Tp31b0RlW8aKq2Z4VjBRUFYm3PNB87KcjjFcb/z3UhRC0ooEcExVSLjarrts1KJT+maJSvWN644RCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"082a5e2415429d3ffca4995bce8c93bae486c7ca289fc61fc91c4f577c9caca8","last_reissued_at":"2026-05-18T02:44:48.877565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:48.877565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low degree hypersurfaces of projective toric varieties defined over a $C_1$ field have a rational point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Robin Guilbot","submitted_at":"2014-07-25T15:45:49Z","abstract_excerpt":"Quasi algebraically closed fields, or $C_1$ fields, are defined in terms of a low degree condition. 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