{"paper":{"title":"Compact K\\\"ahler manifolds with nef anti-canonical bundle","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Juanyong Wang, Qimin Zhang, Shin-ichi Matsumura, Xiaojun Wu","submitted_at":"2025-06-29T13:02:52Z","abstract_excerpt":"In this paper, we prove that a compact K\\\"ahler manifold $X$ with the nef anti-canonical bundle $-K_{X}$ admits a locally trivial fibration $\\phi \\colon X \\to Y$, where the fiber $F$ is a rationally connected manifold and the base $Y$ is a Calabi--Yau manifold. We introduce a suitable approach that extends the strategy of Cao--H\\\"oring, originally developed for smooth projective varieties, to more general singular K\\\"ahler spaces. A key technical ingredient is a flatness criterion for pseudo-effective sheaves with vanishing first Chern class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23218","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/2506.23218/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"}