{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:V3DGFEZCZ6J6TRCBSVKZQBPQ5U","short_pith_number":"pith:V3DGFEZC","schema_version":"1.0","canonical_sha256":"aec6629322cf93e9c44195559805f0ed0807fac8da3ae5a7af9ccfd9d01a9e9e","source":{"kind":"arxiv","id":"math/0703066","version":2},"attestation_state":"computed","paper":{"title":"Standard isotrivial fibrations with p_g=q=1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Francesco Polizzi","submitted_at":"2007-03-02T18:27:38Z","abstract_excerpt":"A smooth, projective surface $S$ of general type is said to be a \\emph{standard isotrivial fibration} if there exist a finite group $G$ which acts faithfully on two smooth projective curves $C$ and $F$ so that $S$ is isomorphic to the minimal desingularization of $T:=(C \\times F)/G$. If $T$ is smooth then $S=T$ is called a $\\emph{quasi-bundle}$. In this paper we classify the standard isotrivial fibrations with $p_g=q=1$ which are not quasi-bundles, assuming that all the singularities of $T$ are rational double points. As a by-product, we provide several new examples of minimal surfaces of gene"},"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":"math/0703066","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-03-02T18:27:38Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"6332885bb1a05c0ee492bc7141e47bfac39f52df470caaa214bd1638abfdb931","abstract_canon_sha256":"6e0175687d677f10eea6a4871eacd2bea6dc85b903b254c01bc1222f8a454991"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:57.378984Z","signature_b64":"7jOgwycvprrsLkB10BohZAhPRX2iu4dxLM7C7/CH9KvY2lGRkT8LhLvHTR3ylzyzDGG5c3TRWJ/ehQlMMmZCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aec6629322cf93e9c44195559805f0ed0807fac8da3ae5a7af9ccfd9d01a9e9e","last_reissued_at":"2026-05-18T02:51:57.378481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:57.378481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Standard isotrivial fibrations with p_g=q=1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Francesco Polizzi","submitted_at":"2007-03-02T18:27:38Z","abstract_excerpt":"A smooth, projective surface $S$ of general type is said to be a \\emph{standard isotrivial fibration} if there exist a finite group $G$ which acts faithfully on two smooth projective curves $C$ and $F$ so that $S$ is isomorphic to the minimal desingularization of $T:=(C \\times F)/G$. If $T$ is smooth then $S=T$ is called a $\\emph{quasi-bundle}$. In this paper we classify the standard isotrivial fibrations with $p_g=q=1$ which are not quasi-bundles, assuming that all the singularities of $T$ are rational double points. As a by-product, we provide several new examples of minimal surfaces of gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703066","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":"math/0703066","created_at":"2026-05-18T02:51:57.378564+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0703066v2","created_at":"2026-05-18T02:51:57.378564+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0703066","created_at":"2026-05-18T02:51:57.378564+00:00"},{"alias_kind":"pith_short_12","alias_value":"V3DGFEZCZ6J6","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"V3DGFEZCZ6J6TRCB","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"V3DGFEZC","created_at":"2026-05-18T12:25:56.245647+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/V3DGFEZCZ6J6TRCBSVKZQBPQ5U","json":"https://pith.science/pith/V3DGFEZCZ6J6TRCBSVKZQBPQ5U.json","graph_json":"https://pith.science/api/pith-number/V3DGFEZCZ6J6TRCBSVKZQBPQ5U/graph.json","events_json":"https://pith.science/api/pith-number/V3DGFEZCZ6J6TRCBSVKZQBPQ5U/events.json","paper":"https://pith.science/paper/V3DGFEZC"},"agent_actions":{"view_html":"https://pith.science/pith/V3DGFEZCZ6J6TRCBSVKZQBPQ5U","download_json":"https://pith.science/pith/V3DGFEZCZ6J6TRCBSVKZQBPQ5U.json","view_paper":"https://pith.science/paper/V3DGFEZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0703066&json=true","fetch_graph":"https://pith.science/api/pith-number/V3DGFEZCZ6J6TRCBSVKZQBPQ5U/graph.json","fetch_events":"https://pith.science/api/pith-number/V3DGFEZCZ6J6TRCBSVKZQBPQ5U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V3DGFEZCZ6J6TRCBSVKZQBPQ5U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V3DGFEZCZ6J6TRCBSVKZQBPQ5U/action/storage_attestation","attest_author":"https://pith.science/pith/V3DGFEZCZ6J6TRCBSVKZQBPQ5U/action/author_attestation","sign_citation":"https://pith.science/pith/V3DGFEZCZ6J6TRCBSVKZQBPQ5U/action/citation_signature","submit_replication":"https://pith.science/pith/V3DGFEZCZ6J6TRCBSVKZQBPQ5U/action/replication_record"}},"created_at":"2026-05-18T02:51:57.378564+00:00","updated_at":"2026-05-18T02:51:57.378564+00:00"}