{
  "id": "2311.13451",
  "version": "v1",
  "published": "2023-11-22T15:16:33.000Z",
  "updated": "2023-11-22T15:16:33.000Z",
  "title": "Infinite-dimensional flats in the space of positive metrics on an ample line bundle",
  "authors": [
    "Reboulet Rémi",
    "Witt Nyström David"
  ],
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "abstract": "We show that any continuous positive metric on an ample line bundle L lies at the apex of many infinite-dimensional Mabuchi-flat cones. More precisely, given any bounded graded filtration F of the section ring of L, the set of bounded decreasing convex functions on the support of the Duistermaat--Heckman measure of F embeds L^p-isometrically into the space of bounded positive metrics on L with respect to Darvas' d_p distance for all p\\in[1,\\infty), and in particular with respect to the Mabuchi metric (p=2).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-22T15:16:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ample line bundle",
      "positive metric",
      "infinite-dimensional flats",
      "infinite-dimensional mabuchi-flat cones",
      "duistermaat-heckman measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}