{"paper":{"title":"The spaces of K\\\"ahler and holomorphically tamed symplectic forms on closed 4-manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.SG","authors_text":"Shengzhen Ning, Tian-Jun Li","submitted_at":"2026-07-21T06:59:39Z","abstract_excerpt":"This paper investigates the uniqueness, connectedness and openness properties of spaces of K\\\"ahler forms on closed $4$-manifolds, extending discussions in \\cite{Li08,Sal13}. Motivated by the Streets--Tian conjecture concerning the existence of K\\\"ahler metrics on Hermitian-symplectic complex manifolds, we also study holomorphically tamed symplectic forms, which are symplectic forms tamed by some integrable complex structure. We formulate a parallel question and relate it to the corresponding questions for K\\\"ahler-type symplectic forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18778","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/2607.18778/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"}