{
  "id": "1803.05324",
  "version": "v1",
  "published": "2018-03-13T08:23:28.000Z",
  "updated": "2018-03-13T08:23:28.000Z",
  "title": "Jumps of Milnor numbers of Brieskorn-Pham singularities in non-degenerate families",
  "authors": [
    "Tadeusz Krasiński",
    "Justyna Walewska"
  ],
  "comment": "10 pages, 1 figure. arXiv admin note: text overlap with arXiv:1508.02704",
  "categories": [
    "math.AG"
  ],
  "abstract": "The jump of the Milnor number of an isolated singularity $f_{0}$ is the minimal non-zero difference between the Milnor numbers of $f_{0}$ and one of its deformation $(f_{s}).$ In the case $f_{s}$ are non-degenerate singularities we call the jump non-degenerate. We give a formula (an inductive algorithm using diophantine equations) for the non-degenerate jump of $f_{0}$ in the case $f_{0}$ is a convenient singularity with only one $(n-1)$-dimensional face of its Newton diagram which equivalently (in our problem) can be replaced by the Brieskorn-Pham singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-13T08:23:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B07",
      "32S30"
    ],
    "keywords": [
      "milnor number",
      "brieskorn-pham singularities",
      "non-degenerate families",
      "minimal non-zero difference",
      "dimensional face"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}