{"paper":{"title":"On maximal curves that are not quotients of the Hermitian curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Giovanni Zini, Maria Montanucci, Massimo Giulietti","submitted_at":"2015-11-17T11:36:52Z","abstract_excerpt":"For each prime power $\\ell$ the plane curve $\\mathcal X_\\ell$ with equation $Y^{\\ell^2-\\ell+1}=X^{\\ell^2}-X$ is maximal over $\\mathbb{F}_{\\ell^6}$. Garcia and Stichtenoth in 2006 proved that $\\mathcal X_3$ is not Galois covered by the Hermitian curve and raised the same question for $\\mathcal X_\\ell$ with $\\ell>3$; in this paper we show that $\\mathcal X_\\ell$ is not Galois covered by the Hermitian curve for any $\\ell>3$. Analogously, Duursma and Mak proved that the generalized GK curve $\\mathcal C_{\\ell^n}$ over $\\mathbb{F}_{\\ell^{2n}}$ is not a quotient of the Hermitian curve for $\\ell>2$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05353","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"}