{
  "id": "1710.05580",
  "version": "v1",
  "published": "2017-10-16T09:23:47.000Z",
  "updated": "2017-10-16T09:23:47.000Z",
  "title": "Generating series of intersection volumes of special cycles on unitary Shimura varieties",
  "authors": [
    "Zavosh Amir-Khosravi"
  ],
  "comment": "27 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We form a generating series of regularized volumes of intersections of special cycles on a non-compact unitary Shimura variety with a fixed base change cycle. We show that it is a Hilbert modular form by identifying it with a theta integral, which we show converges even though the parameters lie outside the classical convergence range of Weil. By applying the regularized Siegel-Weil formulas of Ichino and Gan-Qiu-Takeda, we show the modular form is the restriction of a hermitian modular form of degree n related to Siegel Eisenstein series on U(n,n). An essential fact used is a computation showing the Kudla-Millson Schwartz function vanishes under the Ikeda map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-16T09:23:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F27",
      "11F30"
    ],
    "keywords": [
      "special cycles",
      "generating series",
      "intersection volumes",
      "kudla-millson schwartz function vanishes",
      "non-compact unitary shimura variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}