{"paper":{"title":"Morse-Novikov cohomology of locally conformally K\\\"ahler surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.DG","authors_text":"Alexandra Otiman","submitted_at":"2016-09-24T20:59:26Z","abstract_excerpt":"We review the properties of the Morse-Novikov cohomology and compute it for all known compact complex surfaces with locally conformally K\\\"ahler metrics. We present explicit computations for the Inoue surfaces $\\mathcal{S}^0$, $\\mathcal{S}^+$, $\\mathcal{S}^-$ and classify the locally conformally K\\\"ahler (and the tamed locally conformally symplectic) forms on $\\mathcal{S}^0$. We prove the nonexistence of LCK metrics with potential and more generally, of $d_\\theta$-exact LCK metrics on Inoue surfaces and Oeljeklaus-Toma manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07675","kind":"arxiv","version":2},"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"}