{"paper":{"title":"On finiteness properties of separating semigroup of real curve","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Matthew Magin","submitted_at":"2025-11-23T17:25:25Z","abstract_excerpt":"A real morphism $f$ from a real algebraic curve $X$ to $\\mathbb{P}^1$ is called separating if $f^{-1}(\\mathbb{R} \\mathbb{P}^1) = \\mathbb{R} X$. A separating morphism defines a covering $\\mathbb{R} X \\to \\mathbb{R} \\mathbb{P}^1$. Let $X_1, \\ldots, X_r$ denote the components of $\\mathbb{R} X$. M. Kummer and K. Shaw defined the separating semigroup of a curve $X$ as the set of all vectors $d(f) = (d_1(f), \\ldots, d_r(f)) \\in \\mathbb{N}^{r}$ where $f$ is a separating morphism $X \\to \\mathbb{P}^1$ and $d_i(f)$ is the degree of the restriction of $f$ to $X_i$.\n  In the present paper we prove that fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.18545","kind":"arxiv","version":4},"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/2511.18545/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"}