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Using it, we prove that all holomorphic geometric structures of affine type on such a manifold $Y$ are locally homogeneous on a non-empty Zariski open subset. Consequently, if the geometric structure is rigid in the sense of Gromov, then the fundament"},"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":"1901.02656","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-09T10:09:53Z","cross_cats_sorted":[],"title_canon_sha256":"adb77836dcab122caa97cea9e7b3a71d1239e6cde02d7612c2d284e6731e4a99","abstract_canon_sha256":"d4fbca21afa09191fad52760e7d3316bf854557e583bfaa08a2d122ccebe674c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:39.875566Z","signature_b64":"jglTXXxbWv7BW0Dp8EsF3+cQUOVlD8o6ZUQQxVHPjhQfmcPr/zTqlFa2kzRxgAwBd1T4BROXvHHPQzRiHjzNBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77143da9e973a90754ebe1357bdb40c221faa71377cf998bc08ef30f7ee85a38","last_reissued_at":"2026-05-17T23:56:39.874998Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:39.874998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Bochner principle and its applications to Fujiki class $\\mathcal C$ manifolds with vanishing first Chern class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Henri Guenancia, Indranil Biswas, Sorin Dumitrescu","submitted_at":"2019-01-09T10:09:53Z","abstract_excerpt":"We prove a Bochner type vanishing theorem for compact complex manifolds $Y$ in Fujiki class $\\mathcal C$, with vanishing first Chern class, that admit a cohomology class $[\\alpha] \\in H^{1,1}(Y,\\mathbb R)$ which is numerically effective (nef) and has positive self-intersection (meaning $\\int_Y \\alpha^n \\,>\\, 0$, where $n\\,=\\,\\dim_{\\mathbb C} Y$). Using it, we prove that all holomorphic geometric structures of affine type on such a manifold $Y$ are locally homogeneous on a non-empty Zariski open subset. 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