{
  "id": "1612.08269",
  "version": "v1",
  "published": "2016-12-25T14:29:48.000Z",
  "updated": "2016-12-25T14:29:48.000Z",
  "title": "On the arc-analytic type of some weighted homogeneous polynomials",
  "authors": [
    "Jean-Baptiste Campesato"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "It is known that the weights of a complex weighted homogeneous polynomial $f$ with isolated singularity are analytic invariants of $(\\mathbb C^d,f^{-1}(0))$. When $d=2,3$ this result holds by assuming merely the topological type instead of the analytic one. G. Fichou and T. Fukui recently proved the following real counterpart: the blow-Nash type of a real singular non-degenerate convenient weighted homogeneous polynomial in three variables determines its weights. The aim of this paper is to generalize the above-cited result with no condition on the number of variables. We work with a characterization of the blow-Nash equivalence called the arc-analytic equivalence. It is an equivalence relation on Nash function germs with no continuous moduli which may be seen as a semialgebraic version of the blow-analytic equivalence of T.-C. Kuo.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-25T14:29:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P20",
      "14B05",
      "32S15",
      "14E18"
    ],
    "keywords": [
      "arc-analytic type",
      "equivalence",
      "real singular non-degenerate convenient",
      "non-degenerate convenient weighted homogeneous polynomial",
      "nash function germs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}