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The pull-back map obtained by this construction is O_Y-linear, uniquely determined by natural universal properties and exists even in cases where the image of f is entirely contained in the singular locus of the target variety Y.\n  One relevant setting covered by the construction is that where f is the inclusion (or normalisation) of the singular locus of Y. As an immediate corollary, we s"},"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":"1210.3255","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-10-11T14:31:58Z","cross_cats_sorted":[],"title_canon_sha256":"b50fbabcfc6d0c06d5e3a0301802bfc8ddb7aa11564bae6752dd06d419867697","abstract_canon_sha256":"b540b28e4bc904256ec47ef34df1c26a146f116d80b0abc9bbdcd9c707a97a78"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:57.165402Z","signature_b64":"ysp/udeQBCI9nx2HKGwjNrgjbk5YNrKuSbpy1RSg2PQ+2Vpcmwnulj1jCIvXTFWFo6qE5WaBkNno05mv9N4UAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b1755f063995c0ce2b91a9bdb93123ad467d33209149b08febb1d343f279480","last_reissued_at":"2026-05-18T03:17:57.164765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:57.164765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pull-back Morphisms for Reflexive Differential Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Stefan Kebekus","submitted_at":"2012-10-11T14:31:58Z","abstract_excerpt":"Let f : X -> Y be a morphism between normal complex varieties, and assume that Y is Kawamata log terminal. Given any differential form, defined on the smooth locus of Y, we construct a \"pull-back form\" on X. The pull-back map obtained by this construction is O_Y-linear, uniquely determined by natural universal properties and exists even in cases where the image of f is entirely contained in the singular locus of the target variety Y.\n  One relevant setting covered by the construction is that where f is the inclusion (or normalisation) of the singular locus of Y. 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