{"paper":{"title":"Separating semigroup of genus 4 curves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"S. Yu. Orevkov","submitted_at":"2024-12-03T14:00:47Z","abstract_excerpt":"A rational function on a real algebraic curve $C$ is called separating if it takes real values only at real points. Such a function defines a covering $\\mathbb R C\\to\\mathbb{RP}^1$. Let $c_1,\\dots,c_r$ be connected components of $\\mathbb R C$. M. Kummer and K. Shaw defined the separating semigroup of $C$ as the set of all sequences $(d_1(f),\\dots,d_r(f))$ where $f$ is a separating function and $d_i(f)$ is the degree of the restriction of $f$ to $c_i$.\n  In the present paper we describe the separating semigroups of all genus 4 curves. For the proofs we consider the canonical embedding of $C$ in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.02460","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.02460/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}