{
  "id": "2308.12869",
  "version": "v1",
  "published": "2023-08-24T15:45:56.000Z",
  "updated": "2023-08-24T15:45:56.000Z",
  "title": "On the transcendental lattices of Hyperkähler manifolds",
  "authors": [
    "Benedetta Piroddi",
    "Ángel David Ríos Ortiz"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We introduce the notion of a Hyper-K\\\"{a}hler manifold $X$ induced by a Hodge structure of K3-type. We explore this notion for the known deformation types of hyper-K\\\"{a}hler manifolds studying those that are induced by a K3 or abelian surface, giving lattice-theoretic criteria to decide whether or not they are birational to a moduli space of sheaves over said surface. We highlight the different behaviors we find for the particular class of hyper-K\\\"{a}hler manifolds of O'Grady type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-24T15:45:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J42"
    ],
    "keywords": [
      "hyperkähler manifolds",
      "transcendental lattices",
      "ogrady type",
      "hodge structure",
      "moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}