{
  "id": "2210.12455",
  "version": "v1",
  "published": "2022-10-22T13:56:40.000Z",
  "updated": "2022-10-22T13:56:40.000Z",
  "title": "On some birational invariants of hyper-Kähler manifolds",
  "authors": [
    "Chenyu Bai"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We study in this article three birational invariants of projective hyper-K\\\"ahler manifolds: the degree of irrationality, the fibering gonality and the fibering genus. We first improve the lower bound in a recent result of Voisin saying that the fibering genus of a Mumford--Tate very general projective hyper-K\\\"ahler manifold is bounded from below by a constant depending on its dimension and the second Betti number. We also study the relations between these birational invariants for projective K3 surfaces of Picard number 1 and study the asymptotic behaviors of their degree of irrationality and fibering genus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-22T13:56:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birational invariants",
      "hyper-kähler manifolds",
      "fibering genus",
      "second betti number",
      "irrationality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}