{"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. Consequently, if the geometric structure is rigid in the sense of Gromov, then the fundament"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02656","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":""},"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"}