{"paper":{"title":"The sigma function for trigonal cyclic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.AG","authors_text":"Emma Previato, Jiryo Komeda, Shigeki Matsutani","submitted_at":"2017-12-03T02:00:56Z","abstract_excerpt":"A recent generalization of the \"Kleinian sigma function\" involves the choice of a point $P$ of a Riemann surface $X$, namely a \"pointed curve\" $(X, P)$. This paper concludes our explicit calculation of the sigma function for curves cyclic trigonal at $P$. We exhibit the Riemann constant for a Weierstrass semigroup at $P$ with minimal set of generators $\\{3, 2r+s,2s+r\\}$, $r<s$, equivalently, non-symmetric, we construct a basis of $H^1(X, \\mathbb{C})$ and a fundamental 2-differential on $X\\times X$, we give the order of vanishing for sigma on Wirtinger strata of the Jacobian of $X$, and a solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00694","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"}