{"paper":{"title":"On the fundamental groups of non-generic $\\mathbb{R}$-join-type curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christophe Eyral, Mutsuo Oka","submitted_at":"2013-07-18T06:11:48Z","abstract_excerpt":"An \\emph{$\\mathbb{R}$-join-type curve} is a curve in $\\mathbb{C}^2$ defined by an equation of the form \\begin{equation*} a\\cdot\\prod_{j=1}^\\ell (y-\\beta_j)^{\\nu_j} = b\\cdot\\prod_{i=1}^m (x-\\alpha_i)^{\\lambda_i}, \\end{equation*} where the coefficients $a$, $b$, $\\alpha_i$ and $\\beta_j$ are \\emph{real} numbers. For generic values of $a$ and $b$, the singular locus of the curve consists of the points $(\\alpha_i,\\beta_j)$ with $\\lambda_i,\\nu_j\\geq 2$ (so-called \\emph{inner} singularities). In the non-generic case, the inner singularities are not the only ones: the curve may also have \\emph{`outer'"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4837","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"}