{
  "id": "2305.18536",
  "version": "v1",
  "published": "2023-05-29T18:08:15.000Z",
  "updated": "2023-05-29T18:08:15.000Z",
  "title": "Duality and polyhedrality of cones for Mori dream spaces",
  "authors": [
    "Maria Chiara Brambilla",
    "Olivia Dumitrescu",
    "Elisa Postinghel",
    "Luis José Santana Sánchez"
  ],
  "comment": "20 pages, 1 figure",
  "categories": [
    "math.AG"
  ],
  "abstract": "Our goal is twofold. On one hand we show that the cones of divisors ample in codimension $k$ on a Mori dream space are rational polyhedral. On the other hand we study the duality between such cones and the cones of $k$-moving curves by means of the Mori chamber decomposition of the former. We give a new proof of the weak duality property (already proved by Payne and Choi) and we exhibit an interesting family of examples for which strong duality holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-29T18:08:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14E05",
      "14E30",
      "14J45"
    ],
    "keywords": [
      "mori dream space",
      "polyhedrality",
      "mori chamber decomposition",
      "weak duality property",
      "strong duality holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}