{
  "id": "2008.09828",
  "version": "v1",
  "published": "2020-08-22T12:55:18.000Z",
  "updated": "2020-08-22T12:55:18.000Z",
  "title": "Equivariant completions of affine spaces",
  "authors": [
    "Ivan Arzhantsev",
    "Yulia Zaitseva"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We survey recent results on open embeddings of the affine space $\\mathbb{C}^n$ into a complete algebraic variety $X$ such that the action of the vector group $\\mathbb{G}_a^n$ on $\\mathbb{C}^n$ by translations extends to an action of $\\mathbb{G}_a^n$ on $X$. The current version of the text includes the introduction and the section on equivariant embeddings into the projective space $\\mathbb{P}^n$. Comments and suggestions are very welcome.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-22T12:55:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "14R10",
      "13E10",
      "14M25",
      "20M32"
    ],
    "keywords": [
      "affine space",
      "equivariant completions",
      "complete algebraic variety",
      "open embeddings",
      "equivariant embeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}