{"paper":{"title":"On the gonality of certain quotient varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jonah Leshin","submitted_at":"2013-09-24T16:00:45Z","abstract_excerpt":"Noether's problem asks whether, for a given field K and finite group G, the fixed field L := K(x_h : h \\in G)^G is a purely transcendental extension of K, where G acts on the x_h by gx_h = x_gh. The field L is naturally the function field of a quotient variety V := V (K,G). In analogy to the case of curves, we define the gonality of V to be the minimal degree of a dominant rational map from V to projective space, which, in a sense, measures the extent to which L may fail to be purely transcendental over K. When G is abelian, we give bounds for the gonality of V (K; G)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6230","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":""},"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"}