{
  "id": "2505.03904",
  "version": "v1",
  "published": "2025-05-06T18:19:03.000Z",
  "updated": "2025-05-06T18:19:03.000Z",
  "title": "Semispecial tensors and quotients of the polydisc",
  "authors": [
    "Patrick Graf",
    "Aryaman Patel"
  ],
  "categories": [
    "math.AG",
    "math.CV",
    "math.DG"
  ],
  "abstract": "Let $X$ be a complex-projective variety with klt singularities and ample canonical divisor. We prove that $X$ is a quotient of the polydisc by a group acting properly discontinuously and freely in codimension one if and only if $X$ admits a semispecial tensor with reduced hypersurface. This extends a result of Catanese and Di Scala to singular spaces, and answers a question raised by these authors. As a key step in the proof, we establish the Bochner principle for holomorphic tensors on klt spaces in the negative K\\\"{a}hler--Einstein case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-06T18:19:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semispecial tensor",
      "ample canonical divisor",
      "klt singularities",
      "di scala",
      "singular spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}