{"paper":{"title":"The Hurwitz curve over a finite field and its Weierstrass points for the morphism of lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Herivelto Borges, Nazar Arakelian, Pietro Speziali","submitted_at":"2018-11-22T16:13:13Z","abstract_excerpt":"For any smooth Hurwitz curve $\\mathcal{H}_n: \\, XY^n+YZ^n+X^nZ=0$ over the finite field $\\mathbb{F}_{p}$, an explict description of its Weierstrass points for the morphism of lines is presented. As a consequence, the full automorphism group ${\\rm Aut}(\\mathcal{H}_n)$, as well as the genera of all Galois subcovers of $\\mathcal{H}_n$, with $n\\neq 3, p^r$, are computed. Finally, a question by F. Torres on plane non nonsingular maximal curves is answered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09224","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"}