{"paper":{"title":"On projective manifolds with semi-positive holomorphic sectional curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DG","authors_text":"Shin-ichi Matsumura","submitted_at":"2018-11-10T03:18:55Z","abstract_excerpt":"In this paper, we establish a structure theorem for a smooth projective variety $X$ with semi-positive holomorphic sectional curvature. Our structure theorem contains the solution for Yau's conjecture and it can be regarded as a natural generalization of the structure theorem proved by Howard-Smyth-Wu and Mok for holomorphic bisectional curvature. Specifically, we prove that $X$ admits a locally trivial morphism $\\phi:X \\to Y$ such that the fiber $F$ is rationally connected and the image $Y$ has a finite \\'etale cover $A \\to Y$ by an abelian variety $A$, by combining the author's previous work"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04182","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"}