{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:3XAHQZ3ZQFW266HBPCGVN4KATQ","short_pith_number":"pith:3XAHQZ3Z","schema_version":"1.0","canonical_sha256":"ddc0786779816daf78e1788d56f1409c2a9a066eb43e6c28e0c8860723341247","source":{"kind":"arxiv","id":"math/0611840","version":2},"attestation_state":"computed","paper":{"title":"Moduli of McKay quiver representations II: Groebner basis techniques","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Alastair Craw, Diane Maclagan, Rekha R. Thomas","submitted_at":"2006-11-27T22:35:47Z","abstract_excerpt":"In this paper we introduce several computational techniques for the study of moduli spaces of McKay quiver representations, making use of Groebner bases and toric geometry. For a finite abelian group G in GL(n,k), let Y_\\theta be the coherent component of the moduli space of \\theta-stable representations of the McKay quiver. Our two main results are as follows: we provide a simple description of the quiver representations corresponding to the torus orbits of Y_\\theta, and, in the case where Y_\\theta equals Nakamura's G-Hilbert scheme, we present explicit equations for a cover by local coordina"},"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/0611840","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-11-27T22:35:47Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"f454569c5f0c9aab560f2468733c761fd514628eb35a1e3c88923607b1defc45","abstract_canon_sha256":"a6e83e7ec2680361532f694d5b79e082e1fc1f24a96d78d91c2894e0eff0bfe0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:42.433823Z","signature_b64":"TYsUv/ab+GjGuzSjiwpK78ihLC0rrtLtvRfXvT1b/5gaXUhLBByX3zI+6PIYsBxtyp19DT7brvAqfeiuV5IdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddc0786779816daf78e1788d56f1409c2a9a066eb43e6c28e0c8860723341247","last_reissued_at":"2026-05-18T04:31:42.433395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:42.433395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moduli of McKay quiver representations II: Groebner basis techniques","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Alastair Craw, Diane Maclagan, Rekha R. Thomas","submitted_at":"2006-11-27T22:35:47Z","abstract_excerpt":"In this paper we introduce several computational techniques for the study of moduli spaces of McKay quiver representations, making use of Groebner bases and toric geometry. For a finite abelian group G in GL(n,k), let Y_\\theta be the coherent component of the moduli space of \\theta-stable representations of the McKay quiver. Our two main results are as follows: we provide a simple description of the quiver representations corresponding to the torus orbits of Y_\\theta, and, in the case where Y_\\theta equals Nakamura's G-Hilbert scheme, we present explicit equations for a cover by local coordina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611840","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":"math/0611840","created_at":"2026-05-18T04:31:42.433453+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0611840v2","created_at":"2026-05-18T04:31:42.433453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611840","created_at":"2026-05-18T04:31:42.433453+00:00"},{"alias_kind":"pith_short_12","alias_value":"3XAHQZ3ZQFW2","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"3XAHQZ3ZQFW266HB","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"3XAHQZ3Z","created_at":"2026-05-18T12:25:53.939244+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/3XAHQZ3ZQFW266HBPCGVN4KATQ","json":"https://pith.science/pith/3XAHQZ3ZQFW266HBPCGVN4KATQ.json","graph_json":"https://pith.science/api/pith-number/3XAHQZ3ZQFW266HBPCGVN4KATQ/graph.json","events_json":"https://pith.science/api/pith-number/3XAHQZ3ZQFW266HBPCGVN4KATQ/events.json","paper":"https://pith.science/paper/3XAHQZ3Z"},"agent_actions":{"view_html":"https://pith.science/pith/3XAHQZ3ZQFW266HBPCGVN4KATQ","download_json":"https://pith.science/pith/3XAHQZ3ZQFW266HBPCGVN4KATQ.json","view_paper":"https://pith.science/paper/3XAHQZ3Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0611840&json=true","fetch_graph":"https://pith.science/api/pith-number/3XAHQZ3ZQFW266HBPCGVN4KATQ/graph.json","fetch_events":"https://pith.science/api/pith-number/3XAHQZ3ZQFW266HBPCGVN4KATQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3XAHQZ3ZQFW266HBPCGVN4KATQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3XAHQZ3ZQFW266HBPCGVN4KATQ/action/storage_attestation","attest_author":"https://pith.science/pith/3XAHQZ3ZQFW266HBPCGVN4KATQ/action/author_attestation","sign_citation":"https://pith.science/pith/3XAHQZ3ZQFW266HBPCGVN4KATQ/action/citation_signature","submit_replication":"https://pith.science/pith/3XAHQZ3ZQFW266HBPCGVN4KATQ/action/replication_record"}},"created_at":"2026-05-18T04:31:42.433453+00:00","updated_at":"2026-05-18T04:31:42.433453+00:00"}