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For the group $G$ of order $3$ we construct examples of both rational and nonrational quotients of both rational and nonrational $G$-minimal cubic surfaces over $\\Bbbk$."},"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":"1506.05138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-06-16T20:20:31Z","cross_cats_sorted":[],"title_canon_sha256":"ab9c4a688541728afb65b21582eb9ebeda488dc436a48e71ce28d9a3f07f47fe","abstract_canon_sha256":"565ed53127db3d4d22558cd39862e5a4502c79b308c24194171494ee0b4d43d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:46:12.996354Z","signature_b64":"cEzkS9qiBRGHz/KBJmZ0EUiHgPmcs/a/IU/V0diBDT4OWInJilvEZc0nBAppZviN2F5bg6yEIPCEszMJjCDKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83970086a1587ba69226b1ccd0a4cca50878ea7b9999428192f3490ac96d3e02","last_reissued_at":"2026-05-18T01:46:12.995629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:46:12.995629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quotients of cubic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrey Trepalin","submitted_at":"2015-06-16T20:20:31Z","abstract_excerpt":"Let $\\Bbbk$ be any field of characteristic zero, $X$ be a cubic surface in $\\mathbb{P}^3_{\\Bbbk}$ and $G$ be a group acting on $X$. 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