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An interesting special case is when $f$ is the identity morphism."},"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":"1305.3569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-15T18:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"0c766e8b587f08ecf9459aed6d0e144c7b84902485639ece0f14b7c883b1177c","abstract_canon_sha256":"35f21b719531977944eb4b2f23227b1368d1f009f13f27a64c87ca57fcab498b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.519283Z","signature_b64":"fr4d1VtgysVxRWhRfTX1SRhncI6KpHI6S8bh7X+HvTWeyTse9lkkLu4r8lD44eQCHBSisewJ11PdLKhXmjN2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a8ee341a3407d1f60cf40b3ffb5252cfe33cc8e06cbaf3b4e4808fe749dce07","last_reissued_at":"2026-05-17T23:53:17.518637Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.518637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Log canonical pairs with good augmented base loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Caucher Birkar, Zhengyu Hu","submitted_at":"2013-05-15T18:05:29Z","abstract_excerpt":"Let $(X,B)$ be a projective log canonical pair such that $B$ is a $\\Q$-divisor, and that there is a surjective morphism $f\\colon X\\to Z$ onto a normal variety $Z$ satisfying: $K_X+B\\sim_\\Q f^*M$ for some $\\Q$-divisor $M$, and the augmented base locus ${\\bf{B_+}}(M)$ does not contain the image of any log canonical centre of $(X,B)$. 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