{
  "id": "2409.09142",
  "version": "v1",
  "published": "2024-09-13T18:53:24.000Z",
  "updated": "2024-09-13T18:53:24.000Z",
  "title": "Abundance and SYZ conjecture in families of hyperkahler manifolds",
  "authors": [
    "Andrey Soldatenkov",
    "Misha Verbitsky"
  ],
  "comment": "25 pages, 2 figures, version 1.0.1",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "Let $L$ be a holomorphic line bundle on a hyperkahler manifold $M$, with $c_1(L)$ nef and not big. SYZ conjecture predicts that $L$ is semiample. We prove that this is true, assuming that $(M,L)$ has a deformation $(M',L')$ with $L'$ semiample. We introduce a version of the Teichmuller space that parametrizes pairs $(M,L)$ up to isotopy. We prove a version of the global Torelli theorem for such Teichmuller spaces and use it to deduce the deformation invariance of semiampleness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-13T18:53:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C26",
      "14J42"
    ],
    "keywords": [
      "hyperkahler manifold",
      "teichmuller space",
      "syz conjecture predicts",
      "holomorphic line bundle",
      "global torelli theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}