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Moreover, if $X$ is $\\mathbb{Q}$-factorial, then any Log Minimal Model Program on $K_X+\\Delta$ with scaling terminates. As an application we prove that a log Fano type variety $X$ with $\\mathbb{Q}$-factorial log canonical singularities is a Mori dream space."},"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":"1712.07219","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-19T21:23:21Z","cross_cats_sorted":[],"title_canon_sha256":"24e6a4c97ad43f807a6246bf6f46824993465a25b45a8aca9fa3ce891821be11","abstract_canon_sha256":"fb660f181157aa7e207db229dc12b2f83cfd4c198ebc3f774f26512b8e2dcdab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:32.815525Z","signature_b64":"w76JpNDJgW2qBFY+s1VPMo2tZc+w9Q/a+R7O9/bYkDHHyPm6Gx33NaqKxj1TZEQaG/MuIUrwwjJYQw7JUHtkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce5852f8a32aaf6392d4e1873c9185b900418400737b8014e939f07a109148d9","last_reissued_at":"2026-05-17T23:44:32.814876Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:32.814876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Log canonical pairs with boundaries containing ample divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Zhengyu Hu","submitted_at":"2017-12-19T21:23:21Z","abstract_excerpt":"Let $(X,\\Delta)$ be a projective log canonical pair such that $\\Delta \\geq A$ where $A \\geq 0$ is an ample $\\mathbb{R}$-divisor. 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