{
  "id": "2310.18925",
  "version": "v1",
  "published": "2023-10-29T07:32:59.000Z",
  "updated": "2023-10-29T07:32:59.000Z",
  "title": "Total positivity for matroid Schubert varieties",
  "authors": [
    "Xuhua He",
    "Connor Simpson",
    "Kaitao Xie"
  ],
  "comment": "Comments welcome!",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We define the totally nonnegative matroid Schubert variety $\\mathcal Y_V$ of a linear subspace $V \\subset \\mathbb R^n$. We show that $\\mathcal Y_V$ is a regular CW complex homeomorphic to a closed ball, with strata indexed by pairs of acyclic flats of the oriented matroid of $V$. This closely resembles the regularity theorem for totally nonnegative generalized flag varieties. As a corollary, we obtain a regular CW structure on the real matroid Schubert variety of $V$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-29T07:32:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P25",
      "05B35",
      "20G20"
    ],
    "keywords": [
      "total positivity",
      "nonnegative generalized flag varieties",
      "real matroid schubert variety",
      "regular cw complex homeomorphic",
      "totally nonnegative matroid schubert variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}