{"paper":{"title":"Large automorphism groups of ordinary curves of even genus in odd characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Maria Montanucci, Pietro Speziali","submitted_at":"2019-08-11T21:34:47Z","abstract_excerpt":"Let $\\mathcal{X}$ be a (projective, non-singular, geometrically irreducible) curve of even genus $g(\\mathcal{X}) \\geq 2$ defined over an algebraically closed field $K$ of odd characteristic $p$. If the $p$-rank $\\gamma(\\mathcal{X})$ equals $g(\\mathcal{X})$, then $\\mathcal{X}$ is \\emph{ordinary}. In this paper, we deal with \\emph{large} automorphism groups $G$ of ordinary curves of even genus. We prove that $|G| < 821.37g(\\mathcal{X})^{7/4}$. The proof of our result is based on the classification of automorphism groups of curves of even genus in positive characteristic, see \\cite{giulietti-korc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.04684","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.04684/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"}