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As an application we consider a local projective contraction f: X -> Z from a variety X with terminal Q-factorial singularities, which contracts a prime divisor E to an isolated Q-factorial singularity $P\\in Z$, such that $-(K_X + (n-3)L)$ is f-ample, for a f-ample Cartier divisor "},"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":"1609.00156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-01T09:27:28Z","cross_cats_sorted":[],"title_canon_sha256":"c27b13fe047681803d43762bbfae96cca6f4ae3b19d0322be65030addf541b29","abstract_canon_sha256":"28f7c52f06bacdba3a514c9e6319c1c621d828b8710b931e7c6ea6a0c90f579c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:42.521424Z","signature_b64":"pKAet/6c5cJjNsr7pl870+QpSv5DWUh58mS0cdmo7FX21ZjyPtFLffI/qKasGIqCAKDMITI8mIi6iE2GltgYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e4ee0e70c21ea92ee6747b2ac31f55328d305dd773c945e1972f8ebd0dc977a","last_reissued_at":"2026-05-18T00:50:42.520716Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:42.520716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lifting Weighted Blow-ups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Marco Andreatta","submitted_at":"2016-09-01T09:27:28Z","abstract_excerpt":"Let f: X -> Z be a local, projective, divisorial contraction between normal varieties of dimension n with Q-factorial singularities. 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