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A scheme structure on $U^{K}_{n}$ is endowed by Donaldson as an algebro-geometric Hamiltonian reduction of ADHM data. In this paper, for $K=SO(N,R)$, $N\\ge5$, we prove that $U^{K}_{n}$ is an irreducible normal variety with smooth locus $M^{K}_{n}$. Hence, together with the author's previous result, the K-theoretic Nekrasov partition function for any simple classical group"},"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":"1606.00707","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-06-02T14:48:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"993e485aef05a7407609eaebc66ab3e2f9beae5e465ce3587831224ae06ed61f","abstract_canon_sha256":"6795ce1795a30c8a296bb399b507af083d9071408c1265a6e28e818fab4ad6dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:17.833174Z","signature_b64":"iK9MI6RF6lANHXQJKVQ4KUHMabD2ji9aRtzQPYiToUn0yK7Gck/ffIv/IriR3DQGikvQ2UWMVWS2mzVDT7HeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4df73e17c8ec2b04d987dbb954f62ca96c3c067dd230d0d4b0204d8ce2193b31","last_reissued_at":"2026-05-18T00:20:17.832561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:17.832561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry of Uhlenbeck partial compactification of orthogonal instanton spaces and the K-theoretic Nekrasov partition functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Jaeyoo Choy","submitted_at":"2016-06-02T14:48:59Z","abstract_excerpt":"Let $M^K_n$ be the moduli space of framed $K$-instantons over $S^4$ with instanton number $n$ when $K$ is a compact simple Lie group of classical type. 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