{"paper":{"title":"Symplectic non-K\\\"ahler manifolds with and without the Hard Lefschetz Condition","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"Adriano Tomassini, Richard Hind","submitted_at":"2026-06-22T23:07:06Z","abstract_excerpt":"In this paper we construct compact manifolds without K\\\"ahler structures that admit both a symplectic form satisfying the Hard Lefschetz Condition (HLC) and another symplectic form that does not. Our construction builds upon the orbifold introduced by Fern\\'andez and Mu\\~noz and its symplectic resolution studied by Cavalcanti, Fern\\'andez, and Mu\\~noz. By considering a one-parameter family of symplectic forms on the orbifold, we show that the corresponding resolved manifolds fail to satisfy the HLC for all parameters. However, after performing a suitable symplectic blowup along a union of tori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23996","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23996/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}