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When M is generic, this is used to show that all Lelong numbers of $\\eta$ vanish. We prove that any hyperkahler manifold with Pic(M) of rank 1 has non-trivial coisotropic subvarieties, if a generator of Pic(M) is parabolic."},"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":"0907.4217","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CV","submitted_at":"2009-07-24T05:20:30Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"b472963c48bc9c7199bfb1088d280503c7dcde635f4b4890f2659aafd5f76d60","abstract_canon_sha256":"c9245c535977e016564e56c32c31d4da47dbeb7f83302fa45a9d7eaf33ec00dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:22.338512Z","signature_b64":"4csxGcfyzIvzzHOtq6vvtDaRgLrLqIGV5aSoAOTEmq8OR7BU6nOevdphiiVTKwhsz5UtAhrrc1cr7vxPpbyyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c94c17db9bf2300a435ccc514aa2d62378200cb0c6536b578f37e225549c229","last_reissued_at":"2026-05-18T02:58:22.337988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:22.337988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parabolic nef currents on hyperkaehler manifolds","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.CV","authors_text":"Misha Verbitsky","submitted_at":"2009-07-24T05:20:30Z","abstract_excerpt":"Let M be a compact, holomorphically symplectic Kahler manifold, and $\\eta$ a (1,1)-current which is nef (a limit of Kahler forms). 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