{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:AUPNAX6H5QYRABUYDWVVKNN57J","short_pith_number":"pith:AUPNAX6H","schema_version":"1.0","canonical_sha256":"051ed05fc7ec311006981dab5535bdfa7aa820d51809ee58100ab368fdbde7ec","source":{"kind":"arxiv","id":"1206.5516","version":1},"attestation_state":"computed","paper":{"title":"Hilbert schemes as moduli of Higgs bundles and local systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michael Groechenig","submitted_at":"2012-06-24T16:16:26Z","abstract_excerpt":"We construct five families of two-dimensional moduli spaces of parabolic Higgs bundles (respectively local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve. We show that the Hilbert scheme of m points of these surfaces is again a moduli space of parabolic Higgs bundles (respectively local systems), confirming a conjecture of Boalch in these cases and extending a result of Gorsky--Nekrasov--Rubtsov. Using the McKay correspondence we establish the autoduality conjecture for the derived categories of the moduli spaces "},"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":"1206.5516","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-24T16:16:26Z","cross_cats_sorted":[],"title_canon_sha256":"822e02430e6e6dd80608325669ebafe365d15f760c285c43bc7f62b8ffce8301","abstract_canon_sha256":"6b4803734a4d742283cd213acb397dbb19b4c06cfa394884d1e4e55839cd7b0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:39.857513Z","signature_b64":"Pig2JQ8zHNpoWEHhfAHaj3pN6qT1cO5+l0MTqFew1T0ujNwuEJ3tT0MJ6S5dBfX5Kw+DIPxQIAnMQnDlVVKcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"051ed05fc7ec311006981dab5535bdfa7aa820d51809ee58100ab368fdbde7ec","last_reissued_at":"2026-05-18T03:52:39.856884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:39.856884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbert schemes as moduli of Higgs bundles and local systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michael Groechenig","submitted_at":"2012-06-24T16:16:26Z","abstract_excerpt":"We construct five families of two-dimensional moduli spaces of parabolic Higgs bundles (respectively local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve. We show that the Hilbert scheme of m points of these surfaces is again a moduli space of parabolic Higgs bundles (respectively local systems), confirming a conjecture of Boalch in these cases and extending a result of Gorsky--Nekrasov--Rubtsov. Using the McKay correspondence we establish the autoduality conjecture for the derived categories of the moduli spaces "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5516","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":"1206.5516","created_at":"2026-05-18T03:52:39.856987+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.5516v1","created_at":"2026-05-18T03:52:39.856987+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5516","created_at":"2026-05-18T03:52:39.856987+00:00"},{"alias_kind":"pith_short_12","alias_value":"AUPNAX6H5QYR","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"AUPNAX6H5QYRABUY","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"AUPNAX6H","created_at":"2026-05-18T12:26:58.693483+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/AUPNAX6H5QYRABUYDWVVKNN57J","json":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J.json","graph_json":"https://pith.science/api/pith-number/AUPNAX6H5QYRABUYDWVVKNN57J/graph.json","events_json":"https://pith.science/api/pith-number/AUPNAX6H5QYRABUYDWVVKNN57J/events.json","paper":"https://pith.science/paper/AUPNAX6H"},"agent_actions":{"view_html":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J","download_json":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J.json","view_paper":"https://pith.science/paper/AUPNAX6H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.5516&json=true","fetch_graph":"https://pith.science/api/pith-number/AUPNAX6H5QYRABUYDWVVKNN57J/graph.json","fetch_events":"https://pith.science/api/pith-number/AUPNAX6H5QYRABUYDWVVKNN57J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J/action/storage_attestation","attest_author":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J/action/author_attestation","sign_citation":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J/action/citation_signature","submit_replication":"https://pith.science/pith/AUPNAX6H5QYRABUYDWVVKNN57J/action/replication_record"}},"created_at":"2026-05-18T03:52:39.856987+00:00","updated_at":"2026-05-18T03:52:39.856987+00:00"}