{"paper":{"title":"Generic orbits, normal bases, and generation degree for fields of rational invariants","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ben Blum-Smith, Harm Derksen","submitted_at":"2025-06-06T00:41:56Z","abstract_excerpt":"For a faithful linear representation $V$ of a finite group $G$ in coprime characteristic, we show that if the field Noether number $\\beta_{\\mathrm{field}}$ is the minimum $d$ such that the invariant polynomials of degree $\\leq d$ generate the field $k(V)^G$ of rational invariants as a field, and the spanning degree $D_\\mathrm{span}$ is the minimum $d$ such that the polynomials of degree $\\leq d$ span the rational function field $k(V)$ as a vector space over $k(V)^G$, then $\\beta_{\\mathrm{field}} \\leq 2D_\\mathrm{span} + 1$, and this is sharp. This generalizes a recent result of Edidin and Katz."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05650","kind":"arxiv","version":3},"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/2506.05650/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"}