{
  "id": "1306.0293",
  "version": "v3",
  "published": "2013-06-03T04:34:15.000Z",
  "updated": "2014-10-31T21:47:57.000Z",
  "title": "A realization for a $\\mathbb{Q}$-Hermitian variation of Hodge structure of Calabi-Yau type with real multiplication",
  "authors": [
    "Zheng Zhang"
  ],
  "comment": "11 pages, final version, to appear in Math. Res. Lett",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that the $\\mathbb{Q}$-descents of the canonical $\\mathbb{R}$-variation of Hodge structure of Calabi-Yau type over a tube domain of type $A$ can be realized as sub-variations of Hodge structure of certain $\\mathbb{Q}$-variations of Hodge structure which are naturally associated to abelian varieties of (generalized) Weil type.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-24T18:51:49.000Z",
      "title": "On motivic realizations of Hermitian variations of Hodge structure of Calabi-Yau type",
      "abstract": "Over every irreducible Hermitian symmetric domain, there is a canonical variation of real Hodge structure of Calabi-Yau type. An interesting question is then whether these variations of Hodge structure occur in algebraic geometry. In this short note, we give a positive answer to the question (in the motivic sense) for the irreducible tube domains $\\mathcal{D}$ of type $\\mathrm{A}$. More specifically, we construct the $\\mathbb{Q}$-descents of the canonical Calabi-Yau variation of real Hodge structure on $\\mathcal{D}$ from abelian varieties of Weil type.",
      "comment": "14 pages, reorganized, comments are welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-10-31T21:47:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "calabi-yau type",
      "hermitian variations",
      "motivic realizations",
      "real hodge structure",
      "hodge structure occur"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.0293Z"
    }
  }
}