{
  "id": "2310.15969",
  "version": "v1",
  "published": "2023-10-24T16:08:13.000Z",
  "updated": "2023-10-24T16:08:13.000Z",
  "title": "The analytic Hasse Principle for certain singular intersections of quadrics in $\\mathbb{P}^9$",
  "authors": [
    "Nuno Arala"
  ],
  "comment": "32 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "For a pair of quadratic forms with rational coefficients in at least $10$ variables, we prove an asymptotic formula for the number of common zeros under the assumption that the two forms determine a projective variety with exactly two (geometric) singular points defined over an imaginary quadratic field. This extends work of Browning and Munshi with the help of automorphic methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-24T16:08:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D72",
      "11P55",
      "11G50"
    ],
    "keywords": [
      "analytic hasse principle",
      "singular intersections",
      "imaginary quadratic field",
      "quadratic forms",
      "extends work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}