{"paper":{"title":"Bergman Kernels and algebraic structure of limit space for a sequence of almost K\\\"{a}hler-Ricci solitons","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Feng Wang, Wenshuai Jiang, Xiaohua Zhu","submitted_at":"2014-01-25T14:41:31Z","abstract_excerpt":"In this paper, we give a lower bound of Bergman kernels for a sequence of almost K\\\"{a}hler-Einstein Fano manifolds, or more general, a sequence of Fano manifolds with almost K\\\"{a}hler-Ricci solitons. This generalizes a result by Donaldson-Sun, Tian for K\\\"{a}hler-Einstein manifolds sequence with positive scalar curvature. As an application of our result, we prove that the Gromov-Hausdorff limit of sequence is homomorphic to a log terminal $Q$-Fano variety which admits a K\\\"{a}hler-Ricci soliton on its smooth part."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6542","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"}