{
  "id": "2308.10553",
  "version": "v1",
  "published": "2023-08-21T08:10:25.000Z",
  "updated": "2023-08-21T08:10:25.000Z",
  "title": "Special Kähler geometry and holomorphic Lagrangian fibrations",
  "authors": [
    "Yang Li",
    "Valentino Tosatti"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "We give a new proof of a theorem of Hwang, showing that the base of a holomorphic Lagrangian fibration of a compact hyperkahler manifold must be the half-dimensional projective space, provided the base is smooth. Our arguments exploit the differential geometry of the special Kahler metric that exists on the base away from the discriminant locus, and use a recent result of Bakker.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-21T08:10:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J42",
      "14D06",
      "14D07",
      "32G20",
      "53C25"
    ],
    "keywords": [
      "holomorphic lagrangian fibration",
      "special kähler geometry",
      "compact hyperkahler manifold",
      "special kahler metric",
      "discriminant locus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}