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We are studying compact complex subvarieties of (M,L), when L is a generic induced complex structure. Under additional assumptions (Obata holonomy contained in SL(n,H), existence of an HKT metric), we prove that (M,L) contains no divisors, and all complex subvarieties of codimension 2 are trianalytic (that is, also hypercomplex)."},"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":"1202.0222","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2012-02-01T17:12:22Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"164a481fb44609c6a24095cf753e8ce24087a922820a493766d2ad9812544623","abstract_canon_sha256":"b43b51227d9c180c99d4ca65b398daaa928ef4dfeaa633e3cb9494390b99d56b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:10.776859Z","signature_b64":"Lkq4Ic4C9OW+Etoy/4h6HphqALI2FzFtrQAwcz+4n3dIJArp/GyHmzzFd9exXFMjUMrPR77fsWadmpMk9Kv9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63ba33d275baa1a29e8f7f90bc0b41c289240adbfb459c8917daf9a441f6183c","last_reissued_at":"2026-05-18T03:50:10.776001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:10.776001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subvarieties of hypercomplex manifolds with holonomy in SL(n,H)","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Andrey Soldatenkov, Misha Verbitsky","submitted_at":"2012-02-01T17:12:22Z","abstract_excerpt":"A hypercomplex manifold M is a manifold with a triple I,J,K of complex structure operators satisfying quaternionic relations. 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