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We use the classification of varieties of maximal sectional regularity of \\cite{BLPS1} to see that these surfaces are either particular divisors on a smooth rational $3$-fold scroll $S(1,1,1)\\subset \\mathbb{P}^5$, or else admit a plane $\\mathbb{F} = \\mathbb{P}^2 \\subset \\ma"},"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":"1502.01770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-06T01:43:23Z","cross_cats_sorted":[],"title_canon_sha256":"5af3dd89d555d368df3528fa4a84794552b3c391ac7e6ae60b1de7c0fb206042","abstract_canon_sha256":"9125ea3699e9e345e033e5eb9fde366860d09be842a1ac3594a41b631f560c94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:50.680919Z","signature_b64":"H/R8KyBGUhpKF5ErMSrQZdDzW9EKnsAbC8HYvQxX+l62xQLu0Bu1eBkIcZ2WzQarjOb5coux894VY9E8RB5+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbffbf832d2524deb5f73ef66a62c1fff009e1ea0940d6926fc7ab06e5751809","last_reissued_at":"2026-05-18T02:27:50.680553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:50.680553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On 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":"2015-02-06T01:43:23Z","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 $\\reg(\\mathcal{C})$ of a general hyperplane section curve $\\mathcal{C} = X \\cap \\mathbb{P}^{r-1}$ takes the maximally possible value $d-r+3$. 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