{
  "id": "2405.04002",
  "version": "v1",
  "published": "2024-05-07T04:43:51.000Z",
  "updated": "2024-05-07T04:43:51.000Z",
  "title": "Quadratic varieties of small codimension",
  "authors": [
    "Kiwamu Watanabe"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AG",
    "math.CV",
    "math.DG"
  ],
  "abstract": "Let $X \\subset \\mathbb P^{n+c}$ be a nondegenerate smooth projective variety of dimension $n$ defined by quadratic equations. For such varieties, P. Ionescu and F. Russo proved the Hartshorne conjecture on complete intersections, which states that X is a complete intersection provided that $n\\geq 2c+1$. As the extremal case, they also classified $X$ with $n=2c$. In this paper, we classify $X$ with $n=2c-1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-07T04:43:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J40",
      "14J45",
      "14M10",
      "14M17",
      "51N35"
    ],
    "keywords": [
      "small codimension",
      "quadratic varieties",
      "complete intersection",
      "nondegenerate smooth projective variety",
      "quadratic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}