{"paper":{"title":"A Lower Bound for the Number of Group Actions on a Compact Riemann Surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"Aaron Wootton, James W. Anderson","submitted_at":"2011-07-18T13:34:36Z","abstract_excerpt":"We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus $\\sigma \\geq 2$ is at least quadratic in $\\sigma$. We do this through the introduction of a coarse signature space, the space $\\mathcal{K}_\\sigma$ of {\\em skeletal signatures} of group actions on compact Riemann surfaces of genus $\\sigma$. We discuss the basic properties of $\\mathcal{K}_\\sigma$ and present a full conjectural description."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3433","kind":"arxiv","version":2},"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"}