{
  "id": "1607.04860",
  "version": "v1",
  "published": "2016-07-17T12:33:16.000Z",
  "updated": "2016-07-17T12:33:16.000Z",
  "title": "Intersection multiplicity, Milnor number and Bernstein's theorem",
  "authors": [
    "Pinaki Mondal"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "We compute the intersection multiplicity at the origin of n generic polynomials (over an algebraically closed field K) with fixed Newton diagrams and present a Bernstein-Kushnirenko type characterization of what it means to be 'generic'. This leads to the 'correct' formulation of non-degeneracy of a polynomial with respect to its Milnor number. As another application we compute the number of isolated solutions (counted with multiplicity) in K^n of n generic polynomials with fixed Newton polytopes, with an explicit characterization of non-degeneracy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-17T12:33:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C17",
      "14B05",
      "32S05"
    ],
    "keywords": [
      "milnor number",
      "intersection multiplicity",
      "bernsteins theorem",
      "generic polynomials",
      "bernstein-kushnirenko type characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}