{
  "id": "1712.04857",
  "version": "v1",
  "published": "2017-12-13T16:46:02.000Z",
  "updated": "2017-12-13T16:46:02.000Z",
  "title": "Constant scalar curvature Kahler metrics on rational surfaces",
  "authors": [
    "Jesus Martinez-Garcia"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "We show that the only projective smooth rational surfaces which admit a constant scalar curvature K\\\"ahler metric for all polarisations are the projective plane and the quadric surface. In particular, we show that all rational surfaces other than those two admit a destabilising slope test configuration, as introduced by Ross and Thomas. We further show that all Hirzebruch surfaces other than the quadric surface and all rational surfaces with Picard rank $3$ do not admit a constant scalar curvature K\\\"ahler metric for any polarisation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-13T16:46:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J26",
      "53C55",
      "14J50",
      "14E05",
      "14E07"
    ],
    "keywords": [
      "constant scalar curvature kahler metrics",
      "quadric surface",
      "projective smooth rational surfaces",
      "destabilising slope test configuration",
      "picard rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}