{"paper":{"title":"Quotients of the Hermitian curve from subgroups of ${\\rm PGU}(3,q)$ without fixed points or triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Giovanni Zini, Maria Montanucci","submitted_at":"2018-04-10T08:33:04Z","abstract_excerpt":"In this paper we deal with the problem of classifying the genera of quotient curves $\\mathcal{H}_q/G$, where $\\mathcal{H}_q$ is the $\\mathbb{F}_{q^2}$-maximal Hermitian curve and $G$ is an automorphism group of $\\mathcal{H}_q$. The groups $G$ considered in the literature fix either a point or a triangle in the plane ${\\rm PG}(2,q^6)$. In this paper, we give a complete list of genera of quotients $\\mathcal{H}_q/G$, when $G \\leq {\\rm Aut}(\\mathcal{H}_q) \\cong {\\rm PGU}(3,q)$ does not leave invariant any point or triangle in the plane. As a result, the classification of subgroups $G$ of ${\\rm PGU"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03398","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"}