{
  "id": "2309.03858",
  "version": "v1",
  "published": "2023-09-07T17:18:19.000Z",
  "updated": "2023-09-07T17:18:19.000Z",
  "title": "Kähler--Einstein metrics on quasi-projective manifolds",
  "authors": [
    "Quang-Tuan Dang",
    "Duc-Viet Vu"
  ],
  "comment": "28 pages, comments are welcome",
  "categories": [
    "math.DG",
    "math.CV"
  ],
  "abstract": "Let $X$ be a compact K\\\"ahler manifold and $D$ be a simple normal crossing divisor on $X$ such that $K_X+D$ is big and nef. We first prove that the singular K\\\"ahler--Einstein metric constructed by Berman--Guenancia is almost-complete on $X \\backslash D$ in the sense of Tian--Yau. In our second main result, we establish the weak convergence of conic K\\\"ahler--Einstein metrics of negative curvature to the above-mentioned metric when $K_X+D$ is merely big, answering partly a recent question posed by Biquard--Guenancia. Potentials of low energy play an important role in our approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-07T17:18:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32U15",
      "32Q15"
    ],
    "keywords": [
      "kähler-einstein metrics",
      "quasi-projective manifolds",
      "second main result",
      "low energy play",
      "simple normal crossing divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}