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By \\Gamma we will denote the group of line bundles L over X such that $L^{\\otimes r}$ is trivial. This group \\Gamma acts on {\\mathcal M}_\\xi(r). We compute the Chen-Ruan cohomology of the corresponding orbifold."},"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":"1009.4009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-21T07:09:06Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"c8e0de057395223283bf9bae032ff3b4e315a2345e54ff2aed6cf04de44d7757","abstract_canon_sha256":"2c600d5539975c45233bfca3a0bf73ee85df8224391d6326c1b89371f5b26140"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:34.722514Z","signature_b64":"Nq0SguyuEokoz7DCSbKbC+gzhoMJ9DXfPLUj2+5PrxR9lFTLlNqfUhyCZRNNjSYxCWjQZVUKVZDBo/ve+CjNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c33085e3e0e00078c6e31ef5d7c4b41588e748eb67c82ec44ed97b56f27116a","last_reissued_at":"2026-05-18T04:40:34.721856Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:34.721856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chen-Ruan cohomology of some moduli spaces, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Indranil Biswas, Mainak Poddar","submitted_at":"2010-09-21T07:09:06Z","abstract_excerpt":"Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and \\xi a holomorphic line bundle on it such that r is not a divisor of degree(\\xi). Let {\\mathcal M}_\\xi(r) denote the moduli space of stable vector bundles over X of rank r and determinant \\xi. By \\Gamma we will denote the group of line bundles L over X such that $L^{\\otimes r}$ is trivial. This group \\Gamma acts on {\\mathcal M}_\\xi(r). We compute the Chen-Ruan cohomology of the corresponding orbifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4009","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":"1009.4009","created_at":"2026-05-18T04:40:34.721941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.4009v1","created_at":"2026-05-18T04:40:34.721941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4009","created_at":"2026-05-18T04:40:34.721941+00:00"},{"alias_kind":"pith_short_12","alias_value":"BQZQQXR6BYAA","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BQZQQXR6BYAAPDDO","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BQZQQXR6","created_at":"2026-05-18T12:26:05.355336+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/BQZQQXR6BYAAPDDOGHXV27CLIF","json":"https://pith.science/pith/BQZQQXR6BYAAPDDOGHXV27CLIF.json","graph_json":"https://pith.science/api/pith-number/BQZQQXR6BYAAPDDOGHXV27CLIF/graph.json","events_json":"https://pith.science/api/pith-number/BQZQQXR6BYAAPDDOGHXV27CLIF/events.json","paper":"https://pith.science/paper/BQZQQXR6"},"agent_actions":{"view_html":"https://pith.science/pith/BQZQQXR6BYAAPDDOGHXV27CLIF","download_json":"https://pith.science/pith/BQZQQXR6BYAAPDDOGHXV27CLIF.json","view_paper":"https://pith.science/paper/BQZQQXR6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.4009&json=true","fetch_graph":"https://pith.science/api/pith-number/BQZQQXR6BYAAPDDOGHXV27CLIF/graph.json","fetch_events":"https://pith.science/api/pith-number/BQZQQXR6BYAAPDDOGHXV27CLIF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BQZQQXR6BYAAPDDOGHXV27CLIF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BQZQQXR6BYAAPDDOGHXV27CLIF/action/storage_attestation","attest_author":"https://pith.science/pith/BQZQQXR6BYAAPDDOGHXV27CLIF/action/author_attestation","sign_citation":"https://pith.science/pith/BQZQQXR6BYAAPDDOGHXV27CLIF/action/citation_signature","submit_replication":"https://pith.science/pith/BQZQQXR6BYAAPDDOGHXV27CLIF/action/replication_record"}},"created_at":"2026-05-18T04:40:34.721941+00:00","updated_at":"2026-05-18T04:40:34.721941+00:00"}