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We construct several families (indeed, connected components of the moduli space) of surfaces $S$ of general type with $p_g=5,6$ whose canonical map has image $\\Sigma$ of very high degree, $d=48$ for $p_g=5$, $d=56$ for $p_g=6$. And a connected component of the moduli space consisting of surfaces $S$ with $K^2_S = 40, p_g=4, q=0$ whose canonical map has always degree $\\geq 2$, and, for the general surface, of degree $2$ onto a canonical surface $Y$ with $K^2_Y = 12, p_g=4, q=0$.\n  The surfaces we consider a"},"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":"1704.01100","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-04-04T16:44:40Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"366e8084eec40c50e548f03ff634db77ead8b57e49bc50460c610d575259d676","abstract_canon_sha256":"be526bdc2b61b4ce1a424d12f8de605907ec5ad4581137aaaf982ef2f8c0cb0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:16.210775Z","signature_b64":"iXZeSkl3YUJalG/nMFv+MReu7FhTxUITAIVH8Usk3cBdBi1bITtAboavIJp9/Xl1kR/2bEAYH7ePSopkemy3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36389f48f729760834471fe35384c500ec2e5443c5d0b086ad0555412bb362c4","last_reissued_at":"2026-05-18T00:47:16.207065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:16.207065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the canonical map of some surfaces isogenous to a product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Fabrizio Catanese (Universitaet Bayreuth)","submitted_at":"2017-04-04T16:44:40Z","abstract_excerpt":"We give new contributions to the existence problem of canonical surfaces of high degree. 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And a connected component of the moduli space consisting of surfaces $S$ with $K^2_S = 40, p_g=4, q=0$ whose canonical map has always degree $\\geq 2$, and, for the general surface, of degree $2$ onto a canonical surface $Y$ with $K^2_Y = 12, p_g=4, q=0$.\n  The surfaces we consider a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01100","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":"1704.01100","created_at":"2026-05-18T00:47:16.207300+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.01100v1","created_at":"2026-05-18T00:47:16.207300+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01100","created_at":"2026-05-18T00:47:16.207300+00:00"},{"alias_kind":"pith_short_12","alias_value":"GY4J6SHXFF3A","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GY4J6SHXFF3AQNCH","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GY4J6SHX","created_at":"2026-05-18T12:31:18.294218+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/GY4J6SHXFF3AQNCHD7RVHBGFAD","json":"https://pith.science/pith/GY4J6SHXFF3AQNCHD7RVHBGFAD.json","graph_json":"https://pith.science/api/pith-number/GY4J6SHXFF3AQNCHD7RVHBGFAD/graph.json","events_json":"https://pith.science/api/pith-number/GY4J6SHXFF3AQNCHD7RVHBGFAD/events.json","paper":"https://pith.science/paper/GY4J6SHX"},"agent_actions":{"view_html":"https://pith.science/pith/GY4J6SHXFF3AQNCHD7RVHBGFAD","download_json":"https://pith.science/pith/GY4J6SHXFF3AQNCHD7RVHBGFAD.json","view_paper":"https://pith.science/paper/GY4J6SHX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.01100&json=true","fetch_graph":"https://pith.science/api/pith-number/GY4J6SHXFF3AQNCHD7RVHBGFAD/graph.json","fetch_events":"https://pith.science/api/pith-number/GY4J6SHXFF3AQNCHD7RVHBGFAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GY4J6SHXFF3AQNCHD7RVHBGFAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GY4J6SHXFF3AQNCHD7RVHBGFAD/action/storage_attestation","attest_author":"https://pith.science/pith/GY4J6SHXFF3AQNCHD7RVHBGFAD/action/author_attestation","sign_citation":"https://pith.science/pith/GY4J6SHXFF3AQNCHD7RVHBGFAD/action/citation_signature","submit_replication":"https://pith.science/pith/GY4J6SHXFF3AQNCHD7RVHBGFAD/action/replication_record"}},"created_at":"2026-05-18T00:47:16.207300+00:00","updated_at":"2026-05-18T00:47:16.207300+00:00"}