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Let $\\mathcal{K}_p$ be the moduli space of primitively polarized $K3$ surfaces $(S,L)$ of genus $p\\geqslant 3$ and $\\mathcal{V}_{p,m,\\delta}\\to \\mathcal{K}_p$ be the universal Severi variety of $\\delta$--nodal irreducible curves in $|mL|$ on $(S,L)\\in \\mathcal{K}_p$. We find conditions on $p, m,\\delta$ for the existence of an irreducible component $\\mathcal{V}$ of $\\mathcal{V}_{p,m,\\delta}$ on which the moduli map $\\psi: \\mathcal{V}\\to \\mathcal{M}_g$ (with $g= m^2 (p -1) + 1-\\delta$) has generically maximal rank different"},"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":"1502.07378","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-25T21:47:32Z","cross_cats_sorted":[],"title_canon_sha256":"e1a85558502b0cba1f92896143fff1ec2920f83601af3ea786613820465c5288","abstract_canon_sha256":"664b941687551314631a610fb13df895da7a01006878f9aeecdaada8eadaff50"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:04.353854Z","signature_b64":"9DBbElI6x4DTqxxLlxgrCA0A7xeZVOcG44av8Y4gpspiaRvdHmlXyMQUQIgIawQhW0NmI9fwNwxj8KC4HnoeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6fac49b36f26b85127b03cacb82d095a69fb90ed10842d41af95e156c15ffdf","last_reissued_at":"2026-05-18T00:52:04.353467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:04.353467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moduli of nodal curves on K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andreas Leopold Knutsen, Ciro Ciliberto, Concettina Galati, Flaminio Flamini","submitted_at":"2015-02-25T21:47:32Z","abstract_excerpt":"We consider modular properties of nodal curves on general $K3$ surfaces. Let $\\mathcal{K}_p$ be the moduli space of primitively polarized $K3$ surfaces $(S,L)$ of genus $p\\geqslant 3$ and $\\mathcal{V}_{p,m,\\delta}\\to \\mathcal{K}_p$ be the universal Severi variety of $\\delta$--nodal irreducible curves in $|mL|$ on $(S,L)\\in \\mathcal{K}_p$. We find conditions on $p, m,\\delta$ for the existence of an irreducible component $\\mathcal{V}$ of $\\mathcal{V}_{p,m,\\delta}$ on which the moduli map $\\psi: \\mathcal{V}\\to \\mathcal{M}_g$ (with $g= m^2 (p -1) + 1-\\delta$) has generically maximal rank different"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07378","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":"1502.07378","created_at":"2026-05-18T00:52:04.353522+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.07378v3","created_at":"2026-05-18T00:52:04.353522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07378","created_at":"2026-05-18T00:52:04.353522+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y35MJGZW6JVY","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y35MJGZW6JVYKET3","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y35MJGZW","created_at":"2026-05-18T12:29:50.041715+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/Y35MJGZW6JVYKET3APFMXAWQSW","json":"https://pith.science/pith/Y35MJGZW6JVYKET3APFMXAWQSW.json","graph_json":"https://pith.science/api/pith-number/Y35MJGZW6JVYKET3APFMXAWQSW/graph.json","events_json":"https://pith.science/api/pith-number/Y35MJGZW6JVYKET3APFMXAWQSW/events.json","paper":"https://pith.science/paper/Y35MJGZW"},"agent_actions":{"view_html":"https://pith.science/pith/Y35MJGZW6JVYKET3APFMXAWQSW","download_json":"https://pith.science/pith/Y35MJGZW6JVYKET3APFMXAWQSW.json","view_paper":"https://pith.science/paper/Y35MJGZW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.07378&json=true","fetch_graph":"https://pith.science/api/pith-number/Y35MJGZW6JVYKET3APFMXAWQSW/graph.json","fetch_events":"https://pith.science/api/pith-number/Y35MJGZW6JVYKET3APFMXAWQSW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y35MJGZW6JVYKET3APFMXAWQSW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y35MJGZW6JVYKET3APFMXAWQSW/action/storage_attestation","attest_author":"https://pith.science/pith/Y35MJGZW6JVYKET3APFMXAWQSW/action/author_attestation","sign_citation":"https://pith.science/pith/Y35MJGZW6JVYKET3APFMXAWQSW/action/citation_signature","submit_replication":"https://pith.science/pith/Y35MJGZW6JVYKET3APFMXAWQSW/action/replication_record"}},"created_at":"2026-05-18T00:52:04.353522+00:00","updated_at":"2026-05-18T00:52:04.353522+00:00"}