{
  "id": "2210.12986",
  "version": "v1",
  "published": "2022-10-24T07:19:49.000Z",
  "updated": "2022-10-24T07:19:49.000Z",
  "title": "Theta functions and adiabatic curvature on an Abelian variety",
  "authors": [
    "Ching-Hao Chang",
    "Jih-Hsin Cheng",
    "I-Hsun Tsai"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "For an ample line bundle $L$ on an Abelian variety $M$, we study the theta functions associated with the family of line bundles $L\\otimes T$ on $M$ indexed by $T\\in \\text{Pic}^{0}(M)$. Combined with an appropriate differential geometric setting, this leads to an explicit curvature computation of the direct image bundle $E$ on $\\text{Pic}^{0}(M)$, whose fiber $E_{T}$ is the vector space spanned by the theta functions for the line bundle $L\\otimes T$ on $M$. Some algebro-geometric properties of $E$ are also remarked.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-24T07:19:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32J25",
      "14K25",
      "32L10",
      "14K30",
      "14F25"
    ],
    "keywords": [
      "theta functions",
      "abelian variety",
      "adiabatic curvature",
      "ample line bundle",
      "direct image bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}