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It is a well-known fact that given a product $X\\times \\mathbb{P}^m$ or a $n$-dimensional variety $Y$ dominating $X$, their degrees of irrationality may be smaller than the degree of irrationality of $X$. In this paper, we focus on smooth surfaces $S\\subset\\mathbb{P}^3$ of degree $d\\geq 5$, and we prove that $irr(S\\times\\mathbb{P}^{m})=irr(S)$ for any positive integer $m$, whereas $irr(Y)<irr(S)$ occurs for some $Y$ dominating $"},"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":"1603.05543","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-03-17T15:42:49Z","cross_cats_sorted":[],"title_canon_sha256":"bb74d8a523302c4cedb97973f47bb454f57ebc91f8d2cf16e248d6f4af9008b2","abstract_canon_sha256":"307ee20ba0dee3feb7afb0d736b74f460294a78ebf514d4cb91eb83745bbd8e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:28.878052Z","signature_b64":"ppIx5HmFFZY1qah7ciSjar54AHvx+U9Nyk6zP7QlMr2h7kX2wQ83Z7t+JPA8rdE76NTNYajCSI2pE/3JFutGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8303dfee6bd2d3355a21f5baa484b1147464196e1e538cfbf7233077e8afe03","last_reissued_at":"2026-05-18T00:40:28.877493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:28.877493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On irrationality of surfaces in $\\mathbb{P}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Bastianelli","submitted_at":"2016-03-17T15:42:49Z","abstract_excerpt":"The degree of irrationality $irr(X)$ of a $n$-dimensional complex projective variety $X$ is the least degree of a dominant rational map $X\\dashrightarrow \\mathbb{P}^n$. 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