{"paper":{"title":"Expanding K\\\"ahler-Ricci solitons coming out of K\\\"ahler cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alix Deruelle, Ronan J. Conlon","submitted_at":"2016-07-12T23:51:08Z","abstract_excerpt":"We give necessary and sufficient conditions for a K\\\"ahler equivariant resolution of a K\\\"ahler cone, with the resolution satisfying one of a number of auxiliary conditions, to admit a unique asymptotically conical (AC) expanding gradient K\\\"ahler-Ricci soliton. In particular, it follows that for any $n\\in\\mathbb{N}_{0}$ and for any negative line bundle $L$ over a compact K\\\"ahler manifold $D$, the total space of the vector bundle $L^{\\oplus (n+1)}$ admits a unique AC expanding gradient K\\\"ahler-Ricci soliton with soliton vector field a positive multiple of the Euler vector field if and only i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03546","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"}