{
  "id": "1909.06924",
  "version": "v1",
  "published": "2019-09-16T01:24:24.000Z",
  "updated": "2019-09-16T01:24:24.000Z",
  "title": "A conjectural bound on the second Betti number for hyper-Kähler manifolds",
  "authors": [
    "Yoon-Joo Kim",
    "Radu Laza"
  ],
  "comment": "8 pages; comments/feedback welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "In previous work, we noted that the known cases of hyper-K\\\"ahler manifolds satisfy a natural condition on the LLV decomposition of the cohomology; informally, the Verbitsky component is the dominant representation in the LLV decomposition. Assuming this condition holds for all hyper-K\\\"ahler manifolds, we obtain an upper bound for the second Betti number in terms of the dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-16T01:24:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second betti number",
      "hyper-kähler manifolds",
      "conjectural bound",
      "llv decomposition",
      "condition holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}