{"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 $\\Gamma=\\pi_1(X)$. Let $\\chi \\colon \\Gamma \\to \\mathbb{R}$ be an additive character. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.06250","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.06250/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}