{"paper":{"title":"On some generalized Fermat curves and chords of an affinely regular polygon inscribed in a hyperbola","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Herivelto Borges, Mariana Coutinho","submitted_at":"2019-05-23T20:32:39Z","abstract_excerpt":"Let $\\mathcal{G}$ be the projective plane curve defined over $\\mathbb{F}_q$ given by $$aX^nY^n-X^nZ^n-Y^nZ^n+bZ^{2n}=0,$$ where $ab\\notin\\{0,1\\}$, and for each $s\\in\\{2,\\ldots,n-1\\}$, let $\\mathcal{D}_s^{P_1,P_2}$ be the base-point-free linear series cut out on $\\mathcal{G}$ by the linear system of all curves of degree $s$ passing through the singular points $P_1=(1:0:0)$ and $P_2=(0:1:0)$ of $\\mathcal{G}$. The present work determines an upper bound for the number $N_q(\\mathcal{G})$ of $\\mathbb{F}_q$-rational points on the nonsingular model of $\\mathcal{G}$ in cases where $\\mathcal{D}_s^{P_1,P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09909","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"}