{"paper":{"title":"The K\\\"ahler-Ricci flow and optimal degenerations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"G\\'abor Sz\\'ekelyhidi, Ruadha\\'i Dervan","submitted_at":"2016-12-21T20:00:25Z","abstract_excerpt":"We prove that on Fano manifolds, the K\\\"ahler-Ricci flow produces a \"most destabilising\" degeneration, with respect to a new stability notion related to the H-functional. This answers questions of Chen-Sun-Wang and He.\n  We give two applications of this result. Firstly, we give a purely algebro-geometric formula for the supremum of Perelman's {\\mu}-functional on Fano manifolds, resolving a conjecture of Tian-Zhang-Zhang-Zhu as a special case. Secondly, we use this to prove that if a Fano manifold admits a K\\\"ahler-Ricci soliton, then the K\\\"ahler-Ricci flow converges to it modulo the action of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07299","kind":"arxiv","version":5},"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"}