{
  "id": "2305.10768",
  "version": "v1",
  "published": "2023-05-18T07:22:04.000Z",
  "updated": "2023-05-18T07:22:04.000Z",
  "title": "A note on lcK structures and small deformations of Hopf manifolds",
  "authors": [
    "Keizo Hasegawa"
  ],
  "categories": [
    "math.DG"
  ],
  "abstract": "A Hopf manifold is a compact complex manifold of which the universal covering is $\\mathbb{C}^n - \\{0\\}$. In this note we show that any Hopf manifold admits a locally conformally K\\\"ahler structure (shortly lcK structure), by constructing a complex analytic family around a Hopf manifold of diagonal type, which admits a lcK potential, and applying a well known fact (due to Ornea and Verbitsky) that the property of lcK potential is preserved under a complex analytic family over a sufficiently small parameter space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-18T07:22:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lck structure",
      "small deformations",
      "complex analytic family",
      "lck potential",
      "compact complex manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}