{"paper":{"title":"On Rigidity and the Albanese Variety for Parallelizable Manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J\\\"org Winkelmann","submitted_at":"1997-05-05T00:00:00Z","abstract_excerpt":"We study the rigidity questions and the Albanese Variety for Complex Parallelizable Manifolds. Both are related to the study of the cohomology group $H^1(X,\\mathcal O)$. In particular we show that a compact complex parallelizable manifold is rigid iff $b_1(X)=0$ iff Alb$(X)=\\{e\\}$ iff $H^1(X,\\mathcal O)=0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9705215","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"}