{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UP2L5X4JTKX3U5KNKP4UBGQJRQ","short_pith_number":"pith:UP2L5X4J","schema_version":"1.0","canonical_sha256":"a3f4bedf899aafba754d53f9409a098c127bca06b764328ee135dde3823d2bcb","source":{"kind":"arxiv","id":"1501.04410","version":2},"attestation_state":"computed","paper":{"title":"Special birational transformations of type (2,1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Baohua Fu, Jun-Muk Hwang","submitted_at":"2015-01-19T07:11:04Z","abstract_excerpt":"A birational transformation f: P^n --> Z, where Z is a nonsingular variety of Picard number 1, is called a special birational transformation of type (a, b) if f is given by a linear system of degree a, its inverse is given by a linear system of degree b and the base locus S \\subset P^n of f is irreducible and nonsingular.\n  In this paper, we classify special birational transformations of type (2,1). In addition to previous works Alzati-Sierra and Russo on this topic, our proof employs natural C^*-actions on Z in a crucial way. These C^*-actions also relate our result to the problem studied in "},"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":"1501.04410","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-19T07:11:04Z","cross_cats_sorted":[],"title_canon_sha256":"f635a9a45485f562f419df5ca4712718c93cdcc0cce689d2f406e690fcf218a8","abstract_canon_sha256":"f6fb5f3bb2b5b8de27fc1e555d563042fce146c3f1063d38a7f286dc07e2cb42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:52.236690Z","signature_b64":"HouRMjR1WSiJO7G9hkT9oa/g7YOmfSsMlP2oP2kQXsG3NKyn26dT/7k8mjQpMT0uRr/fnHfCtO8zjj47Z2hTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3f4bedf899aafba754d53f9409a098c127bca06b764328ee135dde3823d2bcb","last_reissued_at":"2026-05-18T00:26:52.235830Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:52.235830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Special birational transformations of type (2,1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Baohua Fu, Jun-Muk Hwang","submitted_at":"2015-01-19T07:11:04Z","abstract_excerpt":"A birational transformation f: P^n --> Z, where Z is a nonsingular variety of Picard number 1, is called a special birational transformation of type (a, b) if f is given by a linear system of degree a, its inverse is given by a linear system of degree b and the base locus S \\subset P^n of f is irreducible and nonsingular.\n  In this paper, we classify special birational transformations of type (2,1). In addition to previous works Alzati-Sierra and Russo on this topic, our proof employs natural C^*-actions on Z in a crucial way. These C^*-actions also relate our result to the problem studied in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04410","kind":"arxiv","version":2},"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":"1501.04410","created_at":"2026-05-18T00:26:52.235950+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.04410v2","created_at":"2026-05-18T00:26:52.235950+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04410","created_at":"2026-05-18T00:26:52.235950+00:00"},{"alias_kind":"pith_short_12","alias_value":"UP2L5X4JTKX3","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UP2L5X4JTKX3U5KN","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UP2L5X4J","created_at":"2026-05-18T12:29:44.643036+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/UP2L5X4JTKX3U5KNKP4UBGQJRQ","json":"https://pith.science/pith/UP2L5X4JTKX3U5KNKP4UBGQJRQ.json","graph_json":"https://pith.science/api/pith-number/UP2L5X4JTKX3U5KNKP4UBGQJRQ/graph.json","events_json":"https://pith.science/api/pith-number/UP2L5X4JTKX3U5KNKP4UBGQJRQ/events.json","paper":"https://pith.science/paper/UP2L5X4J"},"agent_actions":{"view_html":"https://pith.science/pith/UP2L5X4JTKX3U5KNKP4UBGQJRQ","download_json":"https://pith.science/pith/UP2L5X4JTKX3U5KNKP4UBGQJRQ.json","view_paper":"https://pith.science/paper/UP2L5X4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.04410&json=true","fetch_graph":"https://pith.science/api/pith-number/UP2L5X4JTKX3U5KNKP4UBGQJRQ/graph.json","fetch_events":"https://pith.science/api/pith-number/UP2L5X4JTKX3U5KNKP4UBGQJRQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UP2L5X4JTKX3U5KNKP4UBGQJRQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UP2L5X4JTKX3U5KNKP4UBGQJRQ/action/storage_attestation","attest_author":"https://pith.science/pith/UP2L5X4JTKX3U5KNKP4UBGQJRQ/action/author_attestation","sign_citation":"https://pith.science/pith/UP2L5X4JTKX3U5KNKP4UBGQJRQ/action/citation_signature","submit_replication":"https://pith.science/pith/UP2L5X4JTKX3U5KNKP4UBGQJRQ/action/replication_record"}},"created_at":"2026-05-18T00:26:52.235950+00:00","updated_at":"2026-05-18T00:26:52.235950+00:00"}