{"paper":{"title":"Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Guilherme Tizziotti, Wanderson Ten\\'orio","submitted_at":"2017-09-01T11:58:30Z","abstract_excerpt":"In this work we study the generalized Weierstrass semigroup $\\widehat{H} (\\mathbf{P}_m)$ at an $m$-tuple $\\mathbf{P}_m = (P_{1}, \\ldots , P_{m})$ of rational points on certain curves admitting a plane model of the form $f(y) = g(x)$ over $\\mathbb{F}_{q}$, where ${f(T),g(T)\\in \\mathbb{F}_q[T]}$. In particular, we compute the generating set $\\widehat{\\Gamma}(\\mathbf{P}_m)$ of $\\widehat{H} (\\mathbf{P}_m)$ and, as a consequence, we explicit a basis for Riemann-Roch spaces of divisors with support in $\\{P_{1}, \\ldots , P_{m}\\}$ on these curves, generalizing results of Maharaj, Matthews, and Pirsic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00263","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"}