{"paper":{"title":"Local projectivity of Lagrangian fibrations on Hyperk\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Frederic Campana","submitted_at":"2017-12-05T20:15:32Z","abstract_excerpt":"We show that if $f:X\\to B$ is a Lagrangian fibration from a compact connected K\\\"ahler hyperk\\\"ahler manifold $X$ onto a projective normal variety $B$, then $f$ is locally projective. This answers a question raised by L. Kamenova and strengthens a former result (\\cite{Ca05}, Proposition 2.1), according to which the smooth fibres of $f$ are projective. The proof below does not use the known additional results concerning fibres and base in this specific context)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01902","kind":"arxiv","version":2},"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"}