{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BSGQUAHDEFE53NWAZMO2HTXGTG","short_pith_number":"pith:BSGQUAHD","schema_version":"1.0","canonical_sha256":"0c8d0a00e32149ddb6c0cb1da3cee699bf6bca3d86849ad1b916524920ec4666","source":{"kind":"arxiv","id":"1802.01201","version":2},"attestation_state":"computed","paper":{"title":"Moduli of non-standard Nikulin surfaces in low genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro Verra, Andreas Leopold Knutsen, Margherita Lelli-Chiesa","submitted_at":"2018-02-04T21:40:23Z","abstract_excerpt":"Primitively polarized genus $g$ Nikulin surfaces $(S,M,H)$ are of two types, that we call standard and non-standard depending on whether the lattice embedding $\\mathbb{Z}[H] \\oplus_{\\perp} \\mathbf{N} \\subset \\rm{Pic}(S)$ is primitive. Here $H$ is the genus $g$ polarization and $\\mathbf{N}$ is the Nikulin lattice. We concentrate on the non-standard case, which only occurs in odd genus. In particular, we study the birational geometry of the moduli space of non-standard Nikulin surfaces of genus $g$ and prove its rationality for $g=7,11$ and the existence of a rational double cover of it when $g="},"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":"1802.01201","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-04T21:40:23Z","cross_cats_sorted":[],"title_canon_sha256":"8b387d4f96df7dada7354b96b32bf3f1c92fbd557e01841938194a5dd744f73b","abstract_canon_sha256":"4db0cb36907ff198aac753d2d1875f0f9a5e7987783b5c71b7f5f8c9f378794c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:34.566561Z","signature_b64":"O4qJEq6IZJAr86urrSulRVs1QWVH8iy4k8DFwrvLVaZpY8HiziUVPdsYhpzlCChl/+90nAdDSJGjgkx2vpOHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c8d0a00e32149ddb6c0cb1da3cee699bf6bca3d86849ad1b916524920ec4666","last_reissued_at":"2026-05-17T23:55:34.566048Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:34.566048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moduli of non-standard Nikulin surfaces in low genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro Verra, Andreas Leopold Knutsen, Margherita Lelli-Chiesa","submitted_at":"2018-02-04T21:40:23Z","abstract_excerpt":"Primitively polarized genus $g$ Nikulin surfaces $(S,M,H)$ are of two types, that we call standard and non-standard depending on whether the lattice embedding $\\mathbb{Z}[H] \\oplus_{\\perp} \\mathbf{N} \\subset \\rm{Pic}(S)$ is primitive. Here $H$ is the genus $g$ polarization and $\\mathbf{N}$ is the Nikulin lattice. We concentrate on the non-standard case, which only occurs in odd genus. In particular, we study the birational geometry of the moduli space of non-standard Nikulin surfaces of genus $g$ and prove its rationality for $g=7,11$ and the existence of a rational double cover of it when $g="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01201","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":"1802.01201","created_at":"2026-05-17T23:55:34.566130+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.01201v2","created_at":"2026-05-17T23:55:34.566130+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01201","created_at":"2026-05-17T23:55:34.566130+00:00"},{"alias_kind":"pith_short_12","alias_value":"BSGQUAHDEFE5","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BSGQUAHDEFE53NWA","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BSGQUAHD","created_at":"2026-05-18T12:32:16.446611+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/BSGQUAHDEFE53NWAZMO2HTXGTG","json":"https://pith.science/pith/BSGQUAHDEFE53NWAZMO2HTXGTG.json","graph_json":"https://pith.science/api/pith-number/BSGQUAHDEFE53NWAZMO2HTXGTG/graph.json","events_json":"https://pith.science/api/pith-number/BSGQUAHDEFE53NWAZMO2HTXGTG/events.json","paper":"https://pith.science/paper/BSGQUAHD"},"agent_actions":{"view_html":"https://pith.science/pith/BSGQUAHDEFE53NWAZMO2HTXGTG","download_json":"https://pith.science/pith/BSGQUAHDEFE53NWAZMO2HTXGTG.json","view_paper":"https://pith.science/paper/BSGQUAHD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.01201&json=true","fetch_graph":"https://pith.science/api/pith-number/BSGQUAHDEFE53NWAZMO2HTXGTG/graph.json","fetch_events":"https://pith.science/api/pith-number/BSGQUAHDEFE53NWAZMO2HTXGTG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BSGQUAHDEFE53NWAZMO2HTXGTG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BSGQUAHDEFE53NWAZMO2HTXGTG/action/storage_attestation","attest_author":"https://pith.science/pith/BSGQUAHDEFE53NWAZMO2HTXGTG/action/author_attestation","sign_citation":"https://pith.science/pith/BSGQUAHDEFE53NWAZMO2HTXGTG/action/citation_signature","submit_replication":"https://pith.science/pith/BSGQUAHDEFE53NWAZMO2HTXGTG/action/replication_record"}},"created_at":"2026-05-17T23:55:34.566130+00:00","updated_at":"2026-05-17T23:55:34.566130+00:00"}