{
  "id": "1407.7327",
  "version": "v1",
  "published": "2014-07-28T05:45:54.000Z",
  "updated": "2014-07-28T05:45:54.000Z",
  "title": "Monodromy of complete intersections and surface potentials",
  "authors": [
    "Victor A. Vassiliev"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Following Newton, Ivory and Arnold, we study the Newtonian potentials of algebraic hypersurfaces in $R^n$. The ramification of (analytic continuations of) these potential depends on a monodromy group, which can be considered as a proper subgroup of the local monodromy group of a complete intersection (acting on a {\\em twisted} vanishing homology group if $n$ is odd). Studying this monodromy group we prove, in particular, that the attraction force of a hyperbolic layer of degree $d$ in $R^n$ coincides with appropriate algebraic vector-functions everywhere outside the attracting surface if $n=2$ or $d=2$, and is non-algebraic in all domains other than the hyperbolicity domain if the surface is generic and $d\\ge 3$ and $n\\ge 3$ and $n+d \\ge 8$. (Later, W. Ebeling has removed the last restriction $d+n \\ge 8$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-28T05:45:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete intersection",
      "surface potentials",
      "local monodromy group",
      "appropriate algebraic vector-functions",
      "potential depends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.7327V"
    }
  }
}