{"paper":{"title":"Hard Lefschetz property of symplectic structures on compact Kaehler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Yunhyung Cho","submitted_at":"2014-03-06T11:47:58Z","abstract_excerpt":"In this paper, we give a new method to construct a compact symplectic manifold which does not satisfy the hard Lefschetz property.\n  Using our method, we construct a simply connected compact K\\\"ahler manifold $(M,J,\\omega)$ and a symplectic form $\\sigma$ on $M$ which does not satisfy the hard Lefschetz property, but is symplectically deformation equivalent to the K\\\"ahler form $\\omega$.\n  As a consequence, we can give an answer to the question posed by Khesin and McDuff as follows.\n  According to symplectic Hodge theory, any symplectic form $\\omega$ on a smooth manifold $M$ defines \\textit{sym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1418","kind":"arxiv","version":3},"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"}