{
  "id": "1809.03350",
  "version": "v1",
  "published": "2018-09-10T14:28:16.000Z",
  "updated": "2018-09-10T14:28:16.000Z",
  "title": "Detecting tropical defects of polynomial equations",
  "authors": [
    "Paul Görlach",
    "Yue Ren",
    "Jeff Sommars"
  ],
  "categories": [
    "math.AG",
    "cs.SC"
  ],
  "abstract": "We introduce the notion of tropical defects, certificates that a system of polynomial equations is not a tropical basis, and provide algorithms for finding them around affine spaces of complementary dimension to the zero set. We use these techniques to solve open problems regarding del Pezzo surfaces of degree 3 and realizability of valuated gaussoids of rank 4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-10T14:28:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14T05",
      "13P10",
      "68W30"
    ],
    "keywords": [
      "polynomial equations",
      "detecting tropical defects",
      "open problems regarding del pezzo",
      "problems regarding del pezzo surfaces",
      "complementary dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}