{
  "id": "math/9912058",
  "version": "v1",
  "published": "1999-12-07T20:02:43.000Z",
  "updated": "1999-12-07T20:02:43.000Z",
  "title": "Polynomials with general C^2-fibers are variables. I",
  "authors": [
    "Shulim Kaliman"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Suppose that X' is a smooth affine algebraic variety of dimension 3 with H_3(X')=0 which is a UFD and whose invertible functions are constants. Suppose that Z is a Zariski open subset of X which has a morphism p : Z -> U into a curve U such that all fibers of p are isomorphic to C^2. We prove that X' is isomorphic to C^3 iff none of irreducible components of X'-Z has non-isolated singularities. Furthermore, if X' is C^3 then p extends to a polynomial on C^3 which is linear in a suitable coordinate system. As a consequence we obtain the fact formulated in the title of the paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-12-07T20:02:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E09"
    ],
    "keywords": [
      "polynomial",
      "smooth affine algebraic variety",
      "zariski open subset",
      "suitable coordinate system",
      "isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....12058K"
    }
  }
}