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We show that each of these surfaces is either a cone over a curve $C \\subset \\mathbb{P}^{r-1}$ of maximal regularity or else a birational outer linear projection of a smooth rational surface scroll $\\widetilde{X} \\subset \\mathbb{P}^{d+1}$. We prove that the Castelnuovo-Mumford regularity of th"},"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":"1305.2355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-10T14:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"284089e1d3b6262777800496dbfe85bdc1ada8a1d209f2b4090daf1b2cfdcb7e","abstract_canon_sha256":"2b86358c52609eed845d8ca0670022c465b6a694d5b0c1afc75b5010905631a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:00.232150Z","signature_b64":"CHCoh+8bqHo/IYSWIDt8J9S8j07wc9nq7vXJxLvMudMKRVSVco7a5EmwfQDcfyhNNqtosCpKIO0UyCbD+H1+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86a01054ef282a0027ac622e097a766a8228c129867291e04a6503a48c88d525","last_reissued_at":"2026-05-18T03:26:00.231679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:00.231679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Projective surfaces of maximal sectional regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Euisung Park, Markus Brodmann, Peter Schenzel, Wanseok Lee","submitted_at":"2013-05-10T14:49:10Z","abstract_excerpt":"We study projective surfaces $X \\subset \\mathbb{P}^r$ (with $r \\geq 5$) of maximal sectional regularity and degree $d > r$, hence surfaces for which the Castelnuovo-Mumford regularity $\\reg(C)$ of a general hyperplane section curve $C = X \\cap \\mathbb{P}^{r-1}$ takes the maximally possible value $d-r+3$. We show that each of these surfaces is either a cone over a curve $C \\subset \\mathbb{P}^{r-1}$ of maximal regularity or else a birational outer linear projection of a smooth rational surface scroll $\\widetilde{X} \\subset \\mathbb{P}^{d+1}$. 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