{"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). Assume that the cohomology class of $\\eta$ is parabolic, that is, its top power vanishes. We prove that all Lelong sets of $\\eta$ are coisotropic. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.4217","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}