{
  "id": "2006.06211",
  "version": "v1",
  "published": "2020-06-11T05:59:54.000Z",
  "updated": "2020-06-11T05:59:54.000Z",
  "title": "The Hilbert scheme of a pair of linear spaces is a Mori dream space",
  "authors": [
    "Ritvik Ramkumar"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $H_{a,b}^n$ denote the component of the Hilbert scheme whose general point parameterizes an $a$-plane union a $b$-plane meeting transversely in $\\mathbf{P}^n$. We describe the effective and nef cones of $H_{a,b}^n$ and determine when the component is Fano. Moreover, we show that $H_{a,b}^n$ is a Mori dream space for all values of $a,b,n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-11T05:59:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D22",
      "14E05",
      "14E30",
      "14M15"
    ],
    "keywords": [
      "mori dream space",
      "hilbert scheme",
      "linear spaces",
      "general point parameterizes",
      "plane union"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}