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Burman","submitted_at":"2013-11-08T08:56:57Z","abstract_excerpt":"Suppose that $C\\subset\\mathbb P^2$ is a general enough nodal plane curve of degree $>2$, $\\nu\\colon \\hat C\\to C$ is its normalization, and $\\pi\\colon \\hat C\\to\\mathbb P^1$ is a finite morphism simply ramified over the same set of points as a projection $\\mathrm{pr}_p\\circ \\nu\\colon\\hat C \\to\\mathbb P^1$, where $p\\in\\mathbb P^2\\setminus C$ (if $\\mathrm{deg}\\, C=3$, one should assume in addition that $\\deg\\pi\\ne4$). We prove that the morphism $\\pi$ is equivalent to such a projection if and only if it extends to a finite morphism $X\\to(\\mathbb P^2)^*$ ramified over $C^*$, where $X$ is a smooth su"},"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":"1311.1904","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-08T08:56:57Z","cross_cats_sorted":[],"title_canon_sha256":"f84b11013eb6c3e86f7b455cfa8f532f34dbf6ba05fac5d291ff57baedaf8c9f","abstract_canon_sha256":"0bca6bef514cbba36f0b7330b0e8c90133704fddf4deb09fa4f62d13005b9956"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:35.230919Z","signature_b64":"MSlnltbODdDSQEC2TmONrfPJ8vrsV0BdWnG+dgjSSNP8HnXidNUMeiG90xGorCHLBOjfQ4tGf0nk+90zwfrvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"954879cedac1a379bf9062a80e17b4c69f23db673ba8bb370200f5673d04a96b","last_reissued_at":"2026-05-18T03:01:35.230225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:35.230225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On projections of smooth and nodal plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Serge Lvovski, Yu. Burman","submitted_at":"2013-11-08T08:56:57Z","abstract_excerpt":"Suppose that $C\\subset\\mathbb P^2$ is a general enough nodal plane curve of degree $>2$, $\\nu\\colon \\hat C\\to C$ is its normalization, and $\\pi\\colon \\hat C\\to\\mathbb P^1$ is a finite morphism simply ramified over the same set of points as a projection $\\mathrm{pr}_p\\circ \\nu\\colon\\hat C \\to\\mathbb P^1$, where $p\\in\\mathbb P^2\\setminus C$ (if $\\mathrm{deg}\\, C=3$, one should assume in addition that $\\deg\\pi\\ne4$). We prove that the morphism $\\pi$ is equivalent to such a projection if and only if it extends to a finite morphism $X\\to(\\mathbb P^2)^*$ ramified over $C^*$, where $X$ is a smooth su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1904","kind":"arxiv","version":3},"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":"1311.1904","created_at":"2026-05-18T03:01:35.230331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.1904v3","created_at":"2026-05-18T03:01:35.230331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1904","created_at":"2026-05-18T03:01:35.230331+00:00"},{"alias_kind":"pith_short_12","alias_value":"SVEHTTW2YGRX","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SVEHTTW2YGRXTP4Q","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SVEHTTW2","created_at":"2026-05-18T12:27:59.945178+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/SVEHTTW2YGRXTP4QMKUA4F5UY2","json":"https://pith.science/pith/SVEHTTW2YGRXTP4QMKUA4F5UY2.json","graph_json":"https://pith.science/api/pith-number/SVEHTTW2YGRXTP4QMKUA4F5UY2/graph.json","events_json":"https://pith.science/api/pith-number/SVEHTTW2YGRXTP4QMKUA4F5UY2/events.json","paper":"https://pith.science/paper/SVEHTTW2"},"agent_actions":{"view_html":"https://pith.science/pith/SVEHTTW2YGRXTP4QMKUA4F5UY2","download_json":"https://pith.science/pith/SVEHTTW2YGRXTP4QMKUA4F5UY2.json","view_paper":"https://pith.science/paper/SVEHTTW2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.1904&json=true","fetch_graph":"https://pith.science/api/pith-number/SVEHTTW2YGRXTP4QMKUA4F5UY2/graph.json","fetch_events":"https://pith.science/api/pith-number/SVEHTTW2YGRXTP4QMKUA4F5UY2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SVEHTTW2YGRXTP4QMKUA4F5UY2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SVEHTTW2YGRXTP4QMKUA4F5UY2/action/storage_attestation","attest_author":"https://pith.science/pith/SVEHTTW2YGRXTP4QMKUA4F5UY2/action/author_attestation","sign_citation":"https://pith.science/pith/SVEHTTW2YGRXTP4QMKUA4F5UY2/action/citation_signature","submit_replication":"https://pith.science/pith/SVEHTTW2YGRXTP4QMKUA4F5UY2/action/replication_record"}},"created_at":"2026-05-18T03:01:35.230331+00:00","updated_at":"2026-05-18T03:01:35.230331+00:00"}