{
  "id": "1307.4837",
  "version": "v1",
  "published": "2013-07-18T06:11:48.000Z",
  "updated": "2013-07-18T06:11:48.000Z",
  "title": "On the fundamental groups of non-generic $\\mathbb{R}$-join-type curves",
  "authors": [
    "Christophe Eyral",
    "Mutsuo Oka"
  ],
  "comment": "21 pages, 19 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "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'} singularities. The fundamental groups of (the complements of) curves having only inner singularities are considered in \\cite{O}. In the present paper, we investigate the fundamental groups of a special class of curves possessing outer singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-18T06:11:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H30",
      "14H20",
      "14H45",
      "14H50"
    ],
    "keywords": [
      "fundamental groups",
      "join-type curve",
      "inner singularities",
      "curves possessing outer singularities",
      "special class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.4837E"
    }
  }
}