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In this note, we show that $X$ is either a $\\mathbb{P}^1$-bundle over an elliptic curve or a normal cubic surface in $\\mathbb{P}^3.$ Consequently, we give a necessary and sufficient condition for $\\Delta$ to be the branch divisor of a normal triple cover over $\\mathbb{P}^2.$"},"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":"1211.2526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-12T07:42:27Z","cross_cats_sorted":[],"title_canon_sha256":"89787e70566e344d527f86a1dbfb031c881506ba7addeeb8fbb0214d6b3b0133","abstract_canon_sha256":"b6bc3102a03b3e672df1206a667a347fdde26bc1181763c5775a1b23e816e457"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:03.061773Z","signature_b64":"sDthlwypVvsmnNEQxePnyTDYheW7UZicqX+B7wc9UIWwbb+aSfh3tsFQLHvbdDtZV9toVOSMirmvu3ovJRt/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c02950b9eda0e12c8c8099bf3dd1640de7fa3d6949f0defee33d1c1f7e937d97","last_reissued_at":"2026-05-18T03:41:03.061281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:03.061281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on normal triple covers over $\\mathbb{P}^2$ with branch divisors of degree 6","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Taketo Shirane","submitted_at":"2012-11-12T07:42:27Z","abstract_excerpt":"Let $S$ and $T$ be reduced divisors on $\\mathbb{P}^2$ which have no common components, and $\\Delta=S+2\\,T.$ We assume $\\deg\\Delta=6.$ Let $\\pi:X\\to\\mathbb{P}^2$ be a normal triple cover with branch divisor $\\Delta,$ i.e. $\\pi$ is ramified along $S$ (resp. $T$) with the index 2 (resp. 3). In this note, we show that $X$ is either a $\\mathbb{P}^1$-bundle over an elliptic curve or a normal cubic surface in $\\mathbb{P}^3.$ Consequently, we give a necessary and sufficient condition for $\\Delta$ to be the branch divisor of a normal triple cover over $\\mathbb{P}^2.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2526","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.2526","created_at":"2026-05-18T03:41:03.061362+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2526v1","created_at":"2026-05-18T03:41:03.061362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2526","created_at":"2026-05-18T03:41:03.061362+00:00"},{"alias_kind":"pith_short_12","alias_value":"YAUVBOPNUDQS","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_16","alias_value":"YAUVBOPNUDQSZDEA","created_at":"2026-05-18T12:27:27.928770+00:00"},{"alias_kind":"pith_short_8","alias_value":"YAUVBOPN","created_at":"2026-05-18T12:27:27.928770+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YAUVBOPNUDQSZDEATG7T3ULEBX","json":"https://pith.science/pith/YAUVBOPNUDQSZDEATG7T3ULEBX.json","graph_json":"https://pith.science/api/pith-number/YAUVBOPNUDQSZDEATG7T3ULEBX/graph.json","events_json":"https://pith.science/api/pith-number/YAUVBOPNUDQSZDEATG7T3ULEBX/events.json","paper":"https://pith.science/paper/YAUVBOPN"},"agent_actions":{"view_html":"https://pith.science/pith/YAUVBOPNUDQSZDEATG7T3ULEBX","download_json":"https://pith.science/pith/YAUVBOPNUDQSZDEATG7T3ULEBX.json","view_paper":"https://pith.science/paper/YAUVBOPN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2526&json=true","fetch_graph":"https://pith.science/api/pith-number/YAUVBOPNUDQSZDEATG7T3ULEBX/graph.json","fetch_events":"https://pith.science/api/pith-number/YAUVBOPNUDQSZDEATG7T3ULEBX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YAUVBOPNUDQSZDEATG7T3ULEBX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YAUVBOPNUDQSZDEATG7T3ULEBX/action/storage_attestation","attest_author":"https://pith.science/pith/YAUVBOPNUDQSZDEATG7T3ULEBX/action/author_attestation","sign_citation":"https://pith.science/pith/YAUVBOPNUDQSZDEATG7T3ULEBX/action/citation_signature","submit_replication":"https://pith.science/pith/YAUVBOPNUDQSZDEATG7T3ULEBX/action/replication_record"}},"created_at":"2026-05-18T03:41:03.061362+00:00","updated_at":"2026-05-18T03:41:03.061362+00:00"}