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Assume that $(X, C)$ contains a point of type (IIA) and that a general member $H\\in |O_X|$ containing $C$ is normal. We classify such germs in terms of $H$."},"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":"1601.07671","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-28T07:19:26Z","cross_cats_sorted":[],"title_canon_sha256":"5999da24acd98d38ecf691e35594e6f1e4835cd85364284c54fc6c991051df8d","abstract_canon_sha256":"a6dd2032e849ab0273868ae56582e75b7037f68c662cd137a08b23b906faa837"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:04.553744Z","signature_b64":"n4thHyWq2xz1hgP1wDSsFdlw43VShb+V8NkGDcAyNx+ZtXq0cjYwLCPxumhitu5BUyw7XS9rgd7V+atVl8uPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94afbaa18e4fdfce1dfae212bd9a8d313627403c56b4e1d8779a78db88576e90","last_reissued_at":"2026-05-18T00:38:04.553086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:04.553086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Threefold extremal contractions of type (IIA), I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shigefumi Mori, Yuri Prokhorov","submitted_at":"2016-01-28T07:19:26Z","abstract_excerpt":"Let $(X, C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f: (X, C)\\to (Z, o)$ such that $C=f^{-1}(o)_{red}$ and $-K_X$ is ample. 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