{"paper":{"title":"Fundamental groups of compact K\\\"ahler manifolds with semi-positive holomorphic sectional curvature","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DG","authors_text":"Shin-ichi Matsumura","submitted_at":"2025-02-01T08:42:44Z","abstract_excerpt":"In this paper, we prove that a compact K\\\"ahler manifold $X$ with semi-positive holomorphic sectional curvature admits a locally trivial fibration $\\phi \\colon X \\to Y$, where the fiber $F$ is a rationally connected projective manifold and the base $Y$ is a finite \\'etale quotient of a torus. This result extends the structure theorem, previously established for projective manifolds, to compact K\\\"ahler manifolds. A key part of the proof involves analyzing the foliation generated by truly flat tangent vectors and showing the abelianness of the topological fundamental group $\\pi_{1}(X)$, with a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00367","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.00367/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}