{"paper":{"title":"$\\overline\\partial$-Harmonic forms on $4$-dimensional almost-Hermitian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Adriano Tomassini, Nicoletta Tardini","submitted_at":"2021-04-21T15:45:38Z","abstract_excerpt":"Let $(X,J)$ be a $4$-dimensional compact almost-complex manifold and let $g$ be a Hermitian metric on $(X,J)$. Denote by $\\Delta_{\\overline\\partial}:=\\overline\\partial\\overline\\partial^*+\\overline\\partial^*\\overline\\partial$ the $\\overline\\partial$-Laplacian. If $g$ is \\emph{globally conformally K\\\"ahler}, respectively \\emph{(strictly) locally conformally K\\\"ahler}, we prove that the dimension of the space of $\\overline\\partial$-harmonic $(1,1)$-forms on $X$, denoted as $h^{1,1}_{\\overline\\partial}$, is a topological invariant given by $b_-+1$, respectively $b_-$. As an application, we provide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.10594","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.10594/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"}