{
  "id": "1503.01099",
  "version": "v1",
  "published": "2015-03-03T20:52:43.000Z",
  "updated": "2015-03-03T20:52:43.000Z",
  "title": "Singularities of secant varieties",
  "authors": [
    "Chih-Chi Chou",
    "Lei Song"
  ],
  "comment": "13 pages, comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the singularities of the secant variety $\\Sigma(X,L)$ associated to a smooth variety $X$ embedded by a sufficiently positive adjoint bundle $L$. We show that $\\Sigma(X,L)$ is always Du Bois singular. We also give a necessary and sufficient condition for $\\Sigma(X, L)$ to have rational singularities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-03T20:52:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "secant variety",
      "sufficient condition",
      "bois singular",
      "smooth variety",
      "sufficiently positive adjoint bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}