{
  "id": "1308.4381",
  "version": "v1",
  "published": "2013-08-20T19:12:03.000Z",
  "updated": "2013-08-20T19:12:03.000Z",
  "title": "Lower Bounds in Real Schubert Calculus",
  "authors": [
    "Nickolas Hein",
    "Christopher J. Hillar",
    "Frank Sottile"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We describe a large-scale computational experiment to study structure in the numbers of real solutions to osculating instances of Schubert problems. This investigation uncovered Schubert problems whose computed numbers of real solutions variously exhibit nontrivial upper bounds, lower bounds, gaps, and a congruence modulo four. We present a family of Schubert problems, one in each Grassmannian, and prove their osculating instances have the observed lower bounds and gaps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-20T19:12:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N15",
      "14P99"
    ],
    "keywords": [
      "real schubert calculus",
      "lower bounds",
      "real solutions",
      "nontrivial upper bounds",
      "osculating instances"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.4381H"
    }
  }
}