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Our main result is that, if $X$ is a compact 3-dimensional complex manifold with $b_2(X) = 0$ and $a(X) > 0$, then $c_3(X) = \\chi_{\\rm top}(X) = 0$, that is, we either have $b_1(X) = 0, \\ b_3(X) = 2$ or $"},"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":"math/9607215","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"1996-07-08T00:00:00Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"a1e799b4946b78b72434ace6b1ed6c4331aad3e41e9e4af8e23eb93025eac746","abstract_canon_sha256":"d660fa0b3a5ce2031b22824c20e05ce9b99eb77fc87a9069e8c65f0296168df6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:47.205823Z","signature_b64":"o11n+9cN33NI1wlqig6JZLPOxa/QuCFvPDz4CcYmt9jbYN1P1bSuyaDfLVxb5jMBAKHz4jdfsUt/qKZ4pkMICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fe5e8f0902508bf5945466eb122adb68c8216cd50139d5c903d582df6abc4f8","last_reissued_at":"2026-05-18T01:05:47.205184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:47.205184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The algebraic dimension of compact complex threefolds with vanishing second Betti number","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Fr\\'ed\\'eric Campana, Jean-Pierre Demailly, Thomas Peternell","submitted_at":"1996-07-08T00:00:00Z","abstract_excerpt":"We investigate compact complex manifolds of dimension three and second Betti number $b_2(X) = 0$. 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