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If the Lefschetz decomposition is generated by a vector bundle tilting over $Y$ then $\\TD$ is a noncommutative resolution, and if the Lefschetz decomposition is rectangular, then $\\TD$ is a crepant resolution."},"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":"math/0609240","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-09-08T15:15:05Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c82f53ddebf953a9143093f56fd372e40a89b79c4fdac9ba4dc50cbee2f29ba2","abstract_canon_sha256":"e4052198a2c8730a9c3a1197e008a359d1ab8637d736e3bcc2be4c724dd1b987"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:56:32.582242Z","signature_b64":"1CDp9bzLYx3yOhXdll4UGllvgs4eSDKWO3WzjUZH+g2N0g/5x/M53e5mopNkGKDzkmzOg2rtJN3d8Eo8T8/rCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bcca3f3e229fad0a9bf5d4317f1cb623f9146d2332289a364ee7b08f36630b0","last_reissued_at":"2026-07-04T14:56:32.581816Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:56:32.581816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lefschetz decompositions and Categorical resolutions of singularities","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alexander Kuznetsov","submitted_at":"2006-09-08T15:15:05Z","abstract_excerpt":"Let $Y$ be a singular algebraic variety and let $\\TY$ be a resolution of singularities of $Y$. 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