{
  "id": "2212.04110",
  "version": "v1",
  "published": "2022-12-08T07:01:45.000Z",
  "updated": "2022-12-08T07:01:45.000Z",
  "title": "Hodge Laplacian and geometry of Kuranishi family of Fano manifolds",
  "authors": [
    "Akito Futaki",
    "Xiaofeng Sun",
    "Yingying Zhang"
  ],
  "comment": "23 pages",
  "categories": [
    "math.DG",
    "math.AG",
    "math.CV"
  ],
  "abstract": "We first obtain eigenvalue estimates for the Hodge Laplacian on Fano manifolds, which follow from the Bochner-Kodaira formula. Then we apply it to study the geometry of the Kuranishi family of deformations of Fano manifolds. We show that the original K\\\"ahler form remains to be a K\\\"ahler form for other members of the Kuranishi family, and give an explicit formula of the Ricci potential. We also show that our set-up gives another account for the Donaldson-Fujiki picture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-08T07:01:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "32G05",
      "32Q15",
      "53C55"
    ],
    "keywords": [
      "fano manifolds",
      "kuranishi family",
      "hodge laplacian",
      "bochner-kodaira formula",
      "donaldson-fujiki picture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}