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We prove that the ray $[\\chi]$ does not belong to the BNS set $\\Sigma(\\Gamma)$ if and only if it comes as a pullback along an algebraic fibration $f \\colon X \\to \\mathcal{C}$ over a quasi-projective hyperbolic orbicurve $\\mathcal{C}$. We also prove that if $\\pi_1(X)$ admits a solvable quotient which is not virtually nilpotent, there exists a finite \\'etale cover $X_1 \\to X$ and a fibration $f \\colon X_1 \\to \\mathcal{C}$ over a quasi-projective hyperbolic"},"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":"2408.06250","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-12T16:02:02Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"9ccc939d91e486ff527ae92edbe8194ba746887d27835ac5a865e2367dd4c8d5","abstract_canon_sha256":"0e111dfd9ba9c337ef570e8d2ef6f92ed66a21e22b3ee09afd14eb78131c46e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:31.719789Z","signature_b64":"Tw1BDxpXsVjj1PZDydo2NzlQe8fUEUTxKVfONvXQNO5CTYaHSAbtzKy6ETl/MOHNodnH79rOXquVgAQKtWZgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"548099d6499006c36c6bff372ef8d50b3aabdcf442ed1d3d302bd976874ea3c6","last_reissued_at":"2026-07-05T11:22:31.719142Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:31.719142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Bieri-Neumann-Strebel sets of quasi-projective groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Vasily Rogov","submitted_at":"2024-08-12T16:02:02Z","abstract_excerpt":"Let $X$ be a smooth complex quasi-projective variety and $\\Gamma=\\pi_1(X)$. 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