{"paper":{"title":"Degenerations and Stability of K\\\"ahler Structures on Calabi--Yau Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kefeng Liu, Yang Shen","submitted_at":"2026-05-18T08:49:12Z","abstract_excerpt":"In this paper, we study the degeneration and stability of K\\\"ahler structures on Calabi--Yau manifolds, namely compact K\\\"ahler manifolds with trivial canonical bundles, from the viewpoint of deformation theory and Hodge theory. Using the global deformation theory of Calabi--Yau manifolds together with estimates relating the Weil--Petersson distance and Beltrami differentials, we prove that certain limits of Calabi--Yau manifolds remain K\\\"ahler.\n  As applications, we give a new proof of Siu's theorem on the K\\\"ahlerness of K3 surfaces. We further prove that deformation limits of hyperk\\\"ahler"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18065","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/2605.18065/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T23:41:59.259043Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.469670Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"67f9f7a2b62eb1391cf0b621f5a78e3c39494c7f8013c2309b46ac83c8773a11"},"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"}