{"paper":{"title":"Plane non-singular curves with an element of \"large\" order in its automorphism group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eslam Badr, Francesc Bars","submitted_at":"2015-10-21T10:18:47Z","abstract_excerpt":"In this note we determine, for an arbitrary but a fixed degree $d$, an algorithm to list the possible values $m$ for which $M_g^{Pl}(\\mathbb{Z}/m)$ is non-empty where $\\mathbb{Z}/m$ denotes the cyclic group of order $m$. In particular, we prove that $m$ should divide one of the integers: $d-1$, $d$, $d^2-3d+3$, $(d-1)^2$, $d(d-2)$ or $d(d-1)$. Secondly, consider a curve $\\delta\\in M_g^{Pl}$ with $g=(d-1)(d-2)/2$ such that $Aut(\\delta)$ has an element of \"very large\" order, in the sense that this element is of order $d^2-3d+3$, $(d-1)^2$, $d(d-2)$ or $d(d-1)$. Then we investigate the groups $G$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06192","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"}