{
  "id": "1005.4503",
  "version": "v3",
  "published": "2010-05-25T08:03:39.000Z",
  "updated": "2010-11-03T15:18:47.000Z",
  "title": "Invariants of Hypersurface Singularities in Positive Characteristic",
  "authors": [
    "Yousra Boubakri",
    "Gert-Martin Greuel",
    "Thomas Markwig"
  ],
  "comment": "Final corrected version; to appear in Revista Matematica Complutense",
  "journal": "Rev. Math. Comp. 25, 1 (2011), 61-85",
  "doi": "10.1007/s13163-010-0056-1",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We study singularities f in K[[x_1,...,x_n]] over an algebraically closed field K of arbitrary characteristic with respect to right respectively contact equivalence, and we establish that the finiteness of the Milnor respectively the Tjurina number is equivalent to finite determinacy. We give improved bounds for the degree of determinacy in positive characteristic. Moreover, we consider different non-degeneracy conditions of Kouchnirenko, Wall and Beelen-Pellikaan in positive characteristic, and we show that planar Newton non-degenerate singularities satisfy Milnor's formula mu=2 delta-r+1. This implies the absence of wild vanishing cycles in the sense of Deligne.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-11-03T15:18:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "32S10",
      "32S25",
      "58K40"
    ],
    "keywords": [
      "positive characteristic",
      "hypersurface singularities",
      "planar newton non-degenerate singularities satisfy",
      "non-degenerate singularities satisfy milnors formula",
      "newton non-degenerate singularities satisfy milnors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4503B"
    }
  }
}