{
  "id": "1912.12449",
  "version": "v1",
  "published": "2019-12-28T12:10:55.000Z",
  "updated": "2019-12-28T12:10:55.000Z",
  "title": "Geometry of Matroids and Hyperplane Arrangements",
  "authors": [
    "Jaeho Shin"
  ],
  "comment": "46 pages, 24 figures",
  "categories": [
    "math.CO",
    "math.AG",
    "math.MG"
  ],
  "abstract": "There is a trichotomic relation between hyperplane arrangements, convex polytopes and matroids. We expand this theory while resolving the complexity issue expected by Mnev's universality theorem. In particular, we invent a combinatorial apparatus for the geometry of hyperplane arrangements in terms of semilattices and their operations, for instance, puzzle-pieces and the matroidal MMP. We also investigate matroid tilings and their extensions. As an algebro-geometric application, we answer Alexeev's question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-28T12:10:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "05B30",
      "05E99",
      "06A11",
      "06A12",
      "14A10",
      "14E15",
      "14E30",
      "14M15",
      "14N10",
      "14N20",
      "14T05",
      "52B05",
      "52B20",
      "52B40",
      "52B55",
      "52C07",
      "52C22",
      "52C35",
      "52C45"
    ],
    "keywords": [
      "hyperplane arrangements",
      "answer alexeevs question",
      "mnevs universality theorem",
      "convex polytopes",
      "algebro-geometric application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}