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In this paper, we construct a birational morphism from Kirwan's desingularization to Narasimhan-Ramanan's, and prove that the Narasimhan-Ramanan's desingularization (called the moduli space of Hecke cycles) is the intermediate variety between Kirwan's and Seshadri's as was conjectured recently in \\ci"},"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/0404351","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2004-04-20T02:51:46Z","cross_cats_sorted":[],"title_canon_sha256":"3fbef360876804ac7802c4db0d0d5913090ca19d7b583d1570be3f8348c277eb","abstract_canon_sha256":"0e0222c5e2ef94f7012bf0809d1001caf10b239e8254b30cb07d8a575286f608"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:32.803495Z","signature_b64":"emkPWAQblmB7QtwVIkcDc33Pa78VrQpoWfQ9qdanVlH/0bkD8f2FLIewwvMmTxn9fzLQAJdt9wLnBHWfHf6qCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f09227b472ecfc4772fc905b13d5eb93d83788c0f001d6db79fbd6972ea52aed","last_reissued_at":"2026-07-04T14:38:32.803068Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:32.803068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cohomology of the moduli space of Hecke cycles","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Insong Choe, Jaeyoo Choy, Young-Hoon Kiem","submitted_at":"2004-04-20T02:51:46Z","abstract_excerpt":"Let $X$ be a smooth projective curve of genus $g \\ge 3$ and let $M_0$ be the moduli space of semistable bundles over $X$ of rank 2 with trivial determinant. 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