{
  "id": "1405.5161",
  "version": "v1",
  "published": "2014-05-20T17:35:27.000Z",
  "updated": "2014-05-20T17:35:27.000Z",
  "title": "Dynamic alpha-invariants of del Pezzo surfaces",
  "authors": [
    "Ivan Cheltsov",
    "Jesus Martinez-Garcia"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "For every smooth del Pezzo surface $S$, smooth curve $C\\in|-K_{S}|$ and $\\beta\\in(0,1]$, we compute the $\\alpha$-invariant of Tian $\\alpha(S,(1-\\beta)C)$ and prove the existence of K\\\"ahler--Einstein metrics on $S$ with edge singularities along $C$ of angle $2\\pi\\beta$ for $\\beta$ in certain interval. In particular we give lower bounds for the invariant $R(S,C)$, introduced by Donaldson as the supremum of all $\\beta\\in(0,1]$ for which such a metric exists.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-20T17:35:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "32Q20",
      "14J26",
      "14E07",
      "32Q10"
    ],
    "keywords": [
      "dynamic alpha-invariants",
      "smooth del pezzo surface",
      "smooth curve",
      "lower bounds",
      "edge singularities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.5161C"
    }
  }
}