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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2104.10594","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-04-21T15:45:38Z","cross_cats_sorted":[],"title_canon_sha256":"200c6dd9d10ca561ba86b5f1db6309e050d64f7c6c0ab209ab23b5ccd7f52d48","abstract_canon_sha256":"9d7cd06092316eef46c019d7320292ca7a7bd4cb614df631dce60e2388dbf911"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T02:04:58.940955Z","signature_b64":"o3GBHe1kX4h6q9UgDGSI8BE/DJR6iYZxut6ANWG3HtakXbYDV1kmct5956g57m/ncpuTQkLIy6psF5ljmJvjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c804c7522fc9c205282fb9aa192750736824140c27b7075c51a9da8fd4465b6","last_reissued_at":"2026-05-27T02:04:58.938790Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T02:04:58.938790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $b_-$. 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