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(1) If D is Kahler-Einstein, then, applying results from our previous paper, we show that each Kahler class on X\\D contains a unique asymptotically conical Ricci-flat Kahler metric, converging to its tangent cone at infinity at a rate of O(r^{-1-\\epsilon}) if X is smooth. This provides a definitive version of a theorem of Tian and Yau. (2) We in"},"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":"1301.5312","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-22T20:58:53Z","cross_cats_sorted":[],"title_canon_sha256":"e54e4eacc38104b730dd1f98b789f7c0c44c78342cb490f221c462e474b342e4","abstract_canon_sha256":"c800c9d62243df54512b166996745160a22a56569c8738ab089f9b3598a33f7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:00.455061Z","signature_b64":"x32ztXgqIRGf5Mx7tn0FQZI+p3UPENnq2PUB1kL2uXpkdanyUuENgMyBSZZB2rTdvgCNQ6W5BuKYVyJPkJYLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3aeb836264b8a0790f9f8aa3d38ffe13fcbea02a4d858552d7c5169d27e2eaa","last_reissued_at":"2026-05-18T02:32:00.454516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:00.454516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotically conical Calabi-Yau metrics on quasi-projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hans-Joachim Hein, Ronan J. Conlon","submitted_at":"2013-01-22T20:58:53Z","abstract_excerpt":"Let X be a compact Kahler orbifold without \\C-codimension-1 singularities. Let D be a suborbifold divisor in X such that D \\supset Sing(X) and -pK_X = q[D] for some p, q \\in \\N with q > p. Assume that D is Fano. We prove the following two main results. (1) If D is Kahler-Einstein, then, applying results from our previous paper, we show that each Kahler class on X\\D contains a unique asymptotically conical Ricci-flat Kahler metric, converging to its tangent cone at infinity at a rate of O(r^{-1-\\epsilon}) if X is smooth. This provides a definitive version of a theorem of Tian and Yau. 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