{"paper":{"title":"$\\mathbb{F}_{p^2}$-maximal curves with many automorphisms are Galois-covered by the Hermitian curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniele Bartoli, Fernando Torres, Maria Montanucci","submitted_at":"2017-08-13T16:54:20Z","abstract_excerpt":"Let $\\mathbb{F}$ be the finite field of order $q^2$, $q=p^h$ with $p$ prime. It is commonly atribute to J.P. Serre the fact that any curve $\\mathbb{F}$-covered by the Hermitian curve $\\mathcal{H}_{q+1}:\\, y^{q+1}=x^q+x$ is also $\\mathbb{F}$-maximal. Nevertheless, the converse is not true as the Giulietti-Korchm\\'aros example shows provided that $q>8$ and $h\\equiv 0\\pmod{3}$. In this paper, we show that if an $\\mathbb{F}$-maximal curve $\\mathcal{X}$ of genus $g\\geq 2$ where $q=p$ is such that $|Aut(\\mathcal{X})|>84(g-1)$ then $\\mathcal{X}$ is Galois-covered by $\\mathcal{H}_{p+1}$. Also, we show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03933","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"}