{"paper":{"title":"Weierstrass semigroups on the Giulietti-Korchm\\'aros curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Maria Montanucci, Peter Beelen","submitted_at":"2017-08-23T12:17:38Z","abstract_excerpt":"In this article we explicitly determine the structure of the Weierstrass semigroups $H(P)$ for any point $P$ of the Giulietti-Korchm\\'aros curve $\\mathcal{X}$. We show that as the point varies, exactly three possibilities arise: One for the $\\mathbb{F}_{q^2}$-rational points (already known in the literature), one for the $\\mathbb{F}_{q^6} \\setminus \\mathbb{F}_{q^2}$-rational points, and one for all remaining points. As a result, we prove a conjecture concerning the structure of $H(P)$ in case $P$ is an $\\mathbb{F}_{q^6} \\setminus \\mathbb{F}_{q^2}$-rational point. As a corollary we also obtain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06974","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"}