{
  "id": "1601.06211",
  "version": "v1",
  "published": "2016-01-23T00:28:14.000Z",
  "updated": "2016-01-23T00:28:14.000Z",
  "title": "Multigraded Apolarity",
  "authors": [
    "Maciej Gałązka"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We generalize methods to compute various kinds of rank to the case of a toric variety $X$ embedded into projective space using a very ample line bundle $\\mathcal{L}$. We use this to compute rank, border rank, and cactus rank of monomials in $H^0(X, \\mathcal{L})^*$ when $X$ is the Hirzebruch surface $\\mathbb{F}_1$, the weighted projective plane $\\mathbb{P}(1,1,4)$, or a fake projective plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-23T00:28:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "14N15"
    ],
    "keywords": [
      "multigraded apolarity",
      "ample line bundle",
      "cactus rank",
      "border rank",
      "toric variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160106211G"
    }
  }
}