{"paper":{"title":"Ordinary algebraic curves with many automorphisms in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"G\\'abor Korchm\\'aros, Maria Montanucci","submitted_at":"2016-10-17T18:30:43Z","abstract_excerpt":"Let $\\mathcal{X}$ be an ordinary (projective, geometrically irreducible, nonsingular) algebraic curve of genus $\\mathcal{g}(\\mathcal{X}) \\ge 2$ defined over an algebraically closed field $\\mathbb{K}$ of odd characteristic $p$. Let $Aut(\\mathcal{X})$ be the group of all automorphisms of $\\mathcal{X}$ which fix $\\mathbb{K}$ element-wise. For any solvable subgroup $G$ of $Aut(\\mathcal{X})$ we prove that $|G|\\leq 34 (\\mathcal{g}(\\mathcal{X})+1)^{3/2}$. There are known curves attaining this bound up to the constant $34$. For $p$ odd, our result improves the classical Nakajima bound $|G|\\leq 84(\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05252","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":""},"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"}