{
  "id": "0807.5135",
  "version": "v3",
  "published": "2008-07-31T19:45:30.000Z",
  "updated": "2010-01-18T08:18:06.000Z",
  "title": "On some generalizations of Newton non degeneracy for hypersurface singularities",
  "authors": [
    "Dmitry Kerner"
  ],
  "comment": "Final version, to appear in the Journal of the London Mathematical Society. 18 pages; uses packages: amssymb,curves. Some new results were added",
  "journal": "Journal of the London Mathematical Society 2010;",
  "doi": "10.1112/jlms/jdq011",
  "categories": [
    "math.AG"
  ],
  "abstract": "We introduce two generalizations of Newton-non-degenerate (Nnd) singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called topologically Newton-non-degenerate (tNnd) if the local embedded topological singularity type can be restored from a collection of Newton diagrams (for some coordinate choices). A singularity that is not tNnd is called essentially Newton-degenerate. For plane curves we give an explicit characterization of tNnd singularities; for hypersurfaces we provide several examples. Next, we treat the question: whether Nnd or tNnd is a property of singularity types or of particular representatives. Namely, is the non-degeneracy preserved in an equi-singular family? This fact is proved for curves. For hypersurfaces we give an example of a Nnd hypersurface whose equi-singular deformation consists of essentially Newton-degenerate hypersurfaces. Finally, we define the directionally Newton-non-degenerate germs, a subclass of tNnd germs. For such singularities the classical formulas for the Milnor number and the zeta function of the Nnd hypersurface are generalized.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-01-18T08:18:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "14J17",
      "14J70",
      "32S05",
      "32S10",
      "32S25"
    ],
    "keywords": [
      "newton non degeneracy",
      "hypersurface singularity",
      "generalizations",
      "nnd hypersurface",
      "newton-non-degenerate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.5135K"
    }
  }
}