{
  "id": "2201.11268",
  "version": "v1",
  "published": "2022-01-27T01:44:10.000Z",
  "updated": "2022-01-27T01:44:10.000Z",
  "title": "Additive actions on hyperquadrics of corank two",
  "authors": [
    "Yingqi Liu"
  ],
  "journal": "Electron. Res. Arch. 30 (2022), no. 1, 1-34",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a projective variety $X$ in $\\mathbb{P}^{m}$ of dimension $n$, an additive action on $X$ is an effective action of $\\mathbb{G}_{a}^{n}$ on $\\mathbb{P}^{m}$ such that $X$ is $\\mathbb{G}_{a}^{n}$-invariant and the induced action on $X$ has an open orbit. Arzhantsev and Popovskiy have classified additive actions on hyperquadrics of corank 0 or 1. In this paper, we give the classification of additive actions on hyperquadrics of corank 2 whose singularities are not fixed by the $\\mathbb{G}_{a}^{n}$-action.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-27T01:44:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "14J50",
      "15A69"
    ],
    "keywords": [
      "hyperquadrics",
      "open orbit",
      "singularities",
      "projective variety"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}