{"paper":{"title":"Examples of asymptotically conical Ricci-flat K\\\"{a}hler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Craig van Coevering","submitted_at":"2008-12-30T17:28:16Z","abstract_excerpt":"The author has proved that a crepant resolution Y of a Ricci-flat K\\\"{a}hler cone X admits a complete Ricci-flat K\\\"{a}hler metric asymptotic to the cone metric in every K\\\"{a}hler class in H^2_c(Y,\\R). These manifolds are generalizations of the Ricci-flat ALE K\\\"{a}hler spaces known by the work of P. Kronheimer, D. Joyce and others.\n  This article considers further the problem of constructing examples. We show that every 3-dimensional Gorenstein toric K\\\"{a}hler cone admits a crepant resolution for which the above theorem applies. This gives infinitely many examples of asymptotically conical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4745","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"}