{"paper":{"title":"Group Theoretical Characterizations of Rationality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andriy Regeta, Christian Urech, Immanuel van Santen","submitted_at":"2024-09-12T09:18:13Z","abstract_excerpt":"Let X be an irreducible variety and Bir(X) its group of birational transformations. We show that the group structure of Bir(X) determines whether X is rational and whether X is ruled.\n  Additionally, we prove that any Borel subgroup of Bir(X) has derived length at most twice the dimension of X, with equality occurring if and only if X is rational and the Borel subgroup is standard. We also provide examples of non-standard Borel subgroups of Bir(P^n) and Aut(A^n), thereby resolving conjectures by Popov and Furter-Poloni."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.07864","kind":"arxiv","version":1},"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/2409.07864/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"}