{"paper":{"title":"On the classification problem for the genera of quotients of the Hermitian curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesca Dalla Volta, Giovanni Zini, Maria Montanucci","submitted_at":"2018-05-23T13:19:01Z","abstract_excerpt":"In this paper we characterize the genera of those quotient curves $\\mathcal{H}_q/G$ of the $\\mathbb{F}_{q^2}$-maximal Hermitian curve $\\mathcal{H}_q$ for which $G$ is contained in the maximal subgroup $\\mathcal{M}_1$ of ${\\rm Aut}(\\mathcal{H}_q)$ fixing a self-polar triangle, or $q$ is even and $G$ is contained in the maximal subgroup $\\mathcal{M}_2$ of ${\\rm Aut}(\\mathcal{H}_q)$ fixing a pole-polar pair $(P,\\ell)$ with respect to the unitary polarity associated to $\\mathcal{H}_q(\\mathbb{F}_{q^2})$. In this way several new values for the genus of a maximal curve over a finite field are obtaine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09118","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"}