{
  "id": "0911.5428",
  "version": "v3",
  "published": "2009-11-28T21:31:24.000Z",
  "updated": "2012-10-23T17:45:50.000Z",
  "title": "Hodge numbers of Fano threefolds via Landau--Ginzburg models",
  "authors": [
    "Victor Przyjalkowski"
  ],
  "comment": "The paper is now a part of the paper arXiv:0902.4668",
  "categories": [
    "math.AG"
  ],
  "abstract": "For each smooth Fano threefold $X$ with Picard number 1 we consider a weak Landau--Ginzburg model, that is a fibration over $\\mathbb C^1$ given by a certain Laurent polynomial. In the spirit of L. Katzarkov's program we prove that the number of irreducible components of the central fiber of its compactification is $h^{1,2}(X)+1$. In particular, it does not depend on the compactification. The question of dependence on the model is open; however we produce examples of different weak Landau--Ginzburg models for the same variety with the same number of components of the central fiber.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-10-23T17:45:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "14J30",
      "14J33",
      "52B20",
      "14N35",
      "14M25",
      "14D07"
    ],
    "keywords": [
      "hodge numbers",
      "weak landau-ginzburg model",
      "central fiber",
      "smooth fano threefold",
      "produce examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.5428P"
    }
  }
}