{
  "id": "math/9809049",
  "version": "v1",
  "published": "1998-09-10T01:30:39.000Z",
  "updated": "1998-09-10T01:30:39.000Z",
  "title": "Embeddings of curves in the plane",
  "authors": [
    "Vladimir Shpilrain",
    "Jie-Tai Yu"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper, we contribute toward a classification of two-variable polynomials by classifying (up to an automorphism of $C^2$) polynomials whose Newton polygon is either a triangle or a line segment. Our classification has several applications to the study of embeddings of algebraic curves in the plane. In particular, we show that for any $k \\ge 2$, there is an irreducible curve with one place at infinity, which has at least $k$ inequivalent embeddings in $C^2$. Also, upon combining our method with a well-known theorem of Zaidenberg and Lin, we show that one can decide \"almost\" just by inspection whether or not a polynomial fiber is an irreducible simply connected curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-09-10T01:30:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E09",
      "14E25"
    ],
    "keywords": [
      "classification",
      "newton polygon",
      "line segment",
      "algebraic curves",
      "inequivalent embeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......9049S"
    }
  }
}