{"paper":{"title":"Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Herivelto Borges, Nazar Arakelian","submitted_at":"2014-09-30T13:54:37Z","abstract_excerpt":"For each integer $s\\geq 1$, we present a family of curves that are $\\mathbb{F}_q$-Frobenius nonclassical with respect to the linear system of plane curves of degree s. In the case $s = 2$, we give necessary and sufficient conditions for such curves to be $\\mathbb{F}_q$-Frobenius nonclassical with respect to the linear system of conics. In the $\\mathbb{F}_q$-Frobenius nonclassical cases, we determine the exact number of $\\mathbb{F}_q$-rational points. In the remaining cases, an upper bound for the number of $\\mathbb{F}_q$-rational points will follow from St\\\"ohr-Voloch theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8549","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"}