{"paper":{"title":"On the fiber product of Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Angelica Vega, Ruben A. Hidalgo, Sebastian Reyes-Carocca","submitted_at":"2016-11-23T17:00:27Z","abstract_excerpt":"Let $S_{0}, S_{1}$ and $S_{2}$ be connected Riemann surfaces and let $\\beta_{1}:S_{1} \\to S_{0}$ and $\\beta_{2}:S_{2} \\to S_{0}$ be surjective holomorphic maps. The associated fiber product\n  $S_{1} \\times_{(\\beta_{1},\\beta_{2})} S_{2}$ has the structure of a singular Riemann surface, endowed with a canonical map $\\beta$ to $S_{0}$ satisfying that $\\beta_{j} \\circ \\pi_{j}=\\beta$, where $\\pi_{j}$ is coordinate projection onto $S_{j}$. In this paper we provide a Fuchsian description of the fiber product and obtain that if one the maps $\\beta_{j}$ is a regular branched cover, then all its irreduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07880","kind":"arxiv","version":3},"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"}