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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0812.4745","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-12-30T17:28:16Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c4d7b4f66ea32c108a67092904e69f10536589e8eda2418ed65253ee2c319394","abstract_canon_sha256":"035d3822e6429f6654825b1e5f79110967acdacd50d22e8f11735a007ea7fc5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:21.168530Z","signature_b64":"I4QsTj7yjA/LInXB4RUkwwoyHUm7tgg+5MUigoTXjMx8Zs9MCKDCD6aAPdDEJ7uTtcvkaJwnqekOB3p4KlZAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fed12026905320e97debbbc71613967d151a24252753ba5d56750891ac839c2b","last_reissued_at":"2026-05-18T04:31:21.167952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:21.167952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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