{
  "id": "2105.01245",
  "version": "v1",
  "published": "2021-05-04T01:53:12.000Z",
  "updated": "2021-05-04T01:53:12.000Z",
  "title": "The Du Bois complex of a hypersurface and the minimal exponent",
  "authors": [
    "Mircea Mustata",
    "Sebastian Olano",
    "Mihnea Popa",
    "Jakub Witaszek"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the Du Bois complex of a hypersurface $Z$ in a smooth complex algebraic variety in terms of the minimal exponent $\\widetilde{\\alpha}(Z)$ and give various applications. We show that if $\\widetilde{\\alpha}(Z)\\geq p+1$, then the canonical morphism $\\Omega_Z^p\\to \\underline{\\Omega}_Z^p$ is an isomorphism. On the other hand, if $Z$ is singular and $\\widetilde{\\alpha}(Z)>p\\geq 2$, then ${\\mathcal H}^{p-1}(\\underline{\\Omega}_Z^{n-p})\\neq 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-04T01:53:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F10",
      "14F17",
      "14B05",
      "32S35"
    ],
    "keywords": [
      "minimal exponent",
      "bois complex",
      "hypersurface",
      "smooth complex algebraic variety",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}