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A classical conjecture of Newstead and Ramanan states that $ c_i(M_{2,1}(Y))=0$ for $i>2(g-1)$ i.e. the top $2g-1$ Chern classes vanish.\n  The purpose of this paper is to generalize this vanishing result to the rank 3 case by generalizing Gieseker's degeneration method. More precisely, we prove that $c_i(M_{3,1}(Y))=0$ for $i>6g-5$. In other words, the top $3g-3$ Chern classes vanish. Notice that we also have $c_i(M_{3,2}(Y))=0$ for $i>6g-5"},"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/0403033","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2004-03-02T04:24:50Z","cross_cats_sorted":[],"title_canon_sha256":"05e8c501d8e78c4d435dcaba4cf6796a35611efa181c1ca44befe2d82674df86","abstract_canon_sha256":"f347e35cc5aec7516f96d7b661e9eb8359e4f22199aea9d96bc97b6147efdef2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:16.758411Z","signature_b64":"RrX45AJVLyzCYwl7vmoU8Zl3L1mkRhC7wYbbDiIP92htebgzB6XF0NDdkghmSrP/Pht12411Z8JMpEuYITozBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b183eef7b59afa6aa23b15a71e39dad718457c8a6cadea6e64782187027c555","last_reissued_at":"2026-07-04T14:38:16.758012Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:16.758012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vanishing of the top Chern classes of the moduli of vector bundles","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jun Li, Young-Hoon Kiem","submitted_at":"2004-03-02T04:24:50Z","abstract_excerpt":"Let $Y$ be a smooth projective curve of genus $g\\ge 2$ and let $M_{r,d}(Y)$ be the moduli space of stable vector bundles of rank $r$ and degree $d$ on $Y$. A classical conjecture of Newstead and Ramanan states that $ c_i(M_{2,1}(Y))=0$ for $i>2(g-1)$ i.e. the top $2g-1$ Chern classes vanish.\n  The purpose of this paper is to generalize this vanishing result to the rank 3 case by generalizing Gieseker's degeneration method. More precisely, we prove that $c_i(M_{3,1}(Y))=0$ for $i>6g-5$. In other words, the top $3g-3$ Chern classes vanish. 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