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We call \\phi a quadro-quadric special briational transformation if \\phi and \\phi^{-1} are defined by linear subsystems of |\\mathcal{O}_{\\mathbb{P}^{r}}(2)| and |\\mathcal{O}_{Z}(2)| respectively. In this paper we classify quadro-quadric special birational transformations in the cases where either (i) Z is a complete intersection and the base locus scheme of \\phi^{-1} is smooth, or (ii) Z is a hypersurface."},"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":"1503.03385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-11T15:46:58Z","cross_cats_sorted":[],"title_canon_sha256":"49813023441d58a3ed813a5785785390670d10e2e8dcaba43f48c82c2bdfcd07","abstract_canon_sha256":"a5e72321c2b01a762968862551d7aaf818d2be8f06dadd24cf7bd7c55292e78c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:03.732115Z","signature_b64":"yc7r1cPUXZ42fW4w14qV7+uxqLPOgUuxESHMs3O/kkvBq6I4cZxpnzKQuzLuiwUq0dHRf8DTFAJ3LahoMNtXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5e5974825e2005041f6f1e96d1d79fd3072c53271c7ecf5c2073b67c63372cc","last_reissued_at":"2026-05-18T02:25:03.731709Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:03.731709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quadro-quadric special birational transformations from projective spaces to smooth complete intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Qifeng Li","submitted_at":"2015-03-11T15:46:58Z","abstract_excerpt":"Let \\phi: \\mathbb{P}^{r}\\dashrightarrow Z be a birational transformation with a smooth connected base locus scheme, where Z\\subseteq\\mathbb{P}^{r+c} is a nondegenerate prime Fano manifold. 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