{"paper":{"title":"On the spectrum of genera of quotients of the Hermitian curve","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":"2017-03-30T17:43:35Z","abstract_excerpt":"We investigate the genera of quotient curves $\\mathcal H_q/G$ of the $\\mathbb F_{q^2}$-maximal Hermitian curve $\\mathcal H_q$, where $G$ is contained in the maximal subgroup $\\mathcal M_q\\leq{\\rm Aut}(\\mathcal H_q)$ fixing a pole-polar pair $(P,\\ell)$ with respect to the unitary polarity associated with $\\mathcal H_q$. To this aim, a geometric and group-theoretical description of $\\mathcal M_q$ is given. The genera of some other quotients $\\mathcal H_q/G$ with $G\\not\\leq\\mathcal M_q$ are also computed. Thus we obtain new values in the spectrum of genera of $\\mathbb F_{q^2}$-maximal curves. A p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10592","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"}