{
  "id": "2002.12495",
  "version": "v1",
  "published": "2020-02-28T00:42:46.000Z",
  "updated": "2020-02-28T00:42:46.000Z",
  "title": "Spectral convergence in geometric quantization --- the case of toric symplectic manifolds",
  "authors": [
    "Kota Hattori",
    "Mayuko Yamashita"
  ],
  "categories": [
    "math.DG",
    "math.MG",
    "math.SG"
  ],
  "abstract": "In this paper, we show the spectral convergence result of $\\overline{\\partial}$-Laplacians when $(X,\\omega)$ is a compact toric symplectic manifold equipped with the natural prequantum line bundle $L$. We consider a family $\\{ J_s\\}_s$ of $\\omega$-compatible complex structures tending to the large complex structure limit, and obtain the spectral convergence of $\\overline{\\partial}$-Laplacians acting on $L^k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-28T00:42:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D50"
    ],
    "keywords": [
      "geometric quantization",
      "compact toric symplectic manifold",
      "natural prequantum line bundle",
      "large complex structure limit",
      "spectral convergence result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}