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However, in dimension 4, very few crepant resolutions are known. In this paper, we will show several examples of crepant resolutions in dimension 4 and show examples in which Hilb^G(C^4) is blow-up of certain crepant resolutions for C^4/G, or Hilb^G(C^4) has singularity."},"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":"1905.06244","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-15T15:26:48Z","cross_cats_sorted":[],"title_canon_sha256":"9569e8d63942c94773f7157d2c79a9716feb6dad02c42e57d62ca7c3737f76a0","abstract_canon_sha256":"fc81f9cc53e82da488b2f8b202cd81af13999b8a5b9e0afbebb45ea1bb441a39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:28.524246Z","signature_b64":"Kgd9tVMkxhvYoOAREPmGZCeDa1OFK9nHFQd4W4w7EHH+mQudJ4zJxGlJAJ+30Ie8aTalOaMeGRjLTdj/inapBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19fdfac6cafd1f3e8d59937d5c61b079586caf5e2d7d776e698bdc8d430d7f67","last_reissued_at":"2026-05-17T23:44:28.523383Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:28.523383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Crepant resolutions and Hilb^G(C^4) for certain abelian subgroups for SL(4,C)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Y.Sato","submitted_at":"2019-05-15T15:26:48Z","abstract_excerpt":"Let G be a finite subgroup of SL(n,C), then the quotient C^n/G has a Gorenstein canonical singularity. 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