{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:X3XP4TTVOX54NU7Y2LXHEELYDU","short_pith_number":"pith:X3XP4TTV","schema_version":"1.0","canonical_sha256":"beeefe4e7575fbc6d3f8d2ee7211781d29a45e95b467fa6429c21b6064413f01","source":{"kind":"arxiv","id":"math/0311508","version":3},"attestation_state":"computed","paper":{"title":"Surfaces of general type with $p_g=q=1, K^2=8$ and bicanonical map of degree 2","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Polizzi","submitted_at":"2003-11-27T19:13:48Z","abstract_excerpt":"We classify the minimal algebraic surfaces of general type with $p_g=q=1, K^2=8$ and bicanonical map of degree 2. It will turn out that they are isogenous to a product of curves, so that if $S$ is such a surface then there exist two smooth curves $C, F$ and a finite group $G$ acting freely on $C \\times F$ such that $S = (C \\times F)/G$. We describe the $C, F$ and $G$ that occur. In particular the curve $C$ is a hyperelliptic-bielliptic curve of genus 3, and the bicanonical map $\\phi$ of $S$ is composed with the involution $\\sigma$ induced on $S$ by $\\tau \\times id: C \\times F \\longrightarrow C"},"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/0311508","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2003-11-27T19:13:48Z","cross_cats_sorted":[],"title_canon_sha256":"3a9fb5067a2965ac0cbbeb1902d8610446b529cecabd53b3f8bdb1d78b3bae60","abstract_canon_sha256":"44b073b5bf1d8d500bc1332b62c75e5e112966004325f8f02e2a6deba814be7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:57.395954Z","signature_b64":"gPx/d76UExEmCuEZFlDLXXtdkqYUQFH+Lg88rEsQAa345CHDI60Qb18itVtLGw6eZHnH4k9js3761jNM9BzQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beeefe4e7575fbc6d3f8d2ee7211781d29a45e95b467fa6429c21b6064413f01","last_reissued_at":"2026-05-18T02:51:57.395269Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:57.395269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Surfaces of general type with $p_g=q=1, K^2=8$ and bicanonical map of degree 2","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Polizzi","submitted_at":"2003-11-27T19:13:48Z","abstract_excerpt":"We classify the minimal algebraic surfaces of general type with $p_g=q=1, K^2=8$ and bicanonical map of degree 2. It will turn out that they are isogenous to a product of curves, so that if $S$ is such a surface then there exist two smooth curves $C, F$ and a finite group $G$ acting freely on $C \\times F$ such that $S = (C \\times F)/G$. We describe the $C, F$ and $G$ that occur. In particular the curve $C$ is a hyperelliptic-bielliptic curve of genus 3, and the bicanonical map $\\phi$ of $S$ is composed with the involution $\\sigma$ induced on $S$ by $\\tau \\times id: C \\times F \\longrightarrow C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311508","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":"math/0311508","created_at":"2026-05-18T02:51:57.395423+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0311508v3","created_at":"2026-05-18T02:51:57.395423+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0311508","created_at":"2026-05-18T02:51:57.395423+00:00"},{"alias_kind":"pith_short_12","alias_value":"X3XP4TTVOX54","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"X3XP4TTVOX54NU7Y","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"X3XP4TTV","created_at":"2026-05-18T12:25:52.051335+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/X3XP4TTVOX54NU7Y2LXHEELYDU","json":"https://pith.science/pith/X3XP4TTVOX54NU7Y2LXHEELYDU.json","graph_json":"https://pith.science/api/pith-number/X3XP4TTVOX54NU7Y2LXHEELYDU/graph.json","events_json":"https://pith.science/api/pith-number/X3XP4TTVOX54NU7Y2LXHEELYDU/events.json","paper":"https://pith.science/paper/X3XP4TTV"},"agent_actions":{"view_html":"https://pith.science/pith/X3XP4TTVOX54NU7Y2LXHEELYDU","download_json":"https://pith.science/pith/X3XP4TTVOX54NU7Y2LXHEELYDU.json","view_paper":"https://pith.science/paper/X3XP4TTV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0311508&json=true","fetch_graph":"https://pith.science/api/pith-number/X3XP4TTVOX54NU7Y2LXHEELYDU/graph.json","fetch_events":"https://pith.science/api/pith-number/X3XP4TTVOX54NU7Y2LXHEELYDU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X3XP4TTVOX54NU7Y2LXHEELYDU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X3XP4TTVOX54NU7Y2LXHEELYDU/action/storage_attestation","attest_author":"https://pith.science/pith/X3XP4TTVOX54NU7Y2LXHEELYDU/action/author_attestation","sign_citation":"https://pith.science/pith/X3XP4TTVOX54NU7Y2LXHEELYDU/action/citation_signature","submit_replication":"https://pith.science/pith/X3XP4TTVOX54NU7Y2LXHEELYDU/action/replication_record"}},"created_at":"2026-05-18T02:51:57.395423+00:00","updated_at":"2026-05-18T02:51:57.395423+00:00"}