{
  "id": "1405.0106",
  "version": "v2",
  "published": "2014-05-01T06:37:59.000Z",
  "updated": "2014-05-27T11:41:00.000Z",
  "title": "Strong Stability of Cotangent Bundles of Cyclic Covers",
  "authors": [
    "Lingguang Li",
    "Junchao Shentu"
  ],
  "comment": "To appear in Comptes Rendus Math\\'ematique",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth projective variety over an algebraically closed field $k$ of characteristic $p>0$ of $\\dim X\\geq 4$ and Picard number $\\rho(X)=1$. Suppose that $X$ satisfies $H^i(X,F^{m*}_X(\\Omg^j_X)\\otimes\\Ls^{-1})=0$ for any ample line bundle $\\Ls$ on $X$, and any nonnegative integers $m,i,j$ with $0\\leq i+j<\\dim X$, where $F_X:X\\rightarrow X$ is the absolute Frobenius morphism. We prove that by procedures combining taking smooth hypersurfaces of dimension $\\geq 3$ and cyclic covers along smooth divisors, if the resulting smooth projective variety $Y$ has ample (resp. nef) canonical bundle $\\omega_Y$, then $\\Omg_Y$ is strongly stable $($resp. strongly semistable$)$ with respect to any polarization.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-27T11:41:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F17",
      "14G17",
      "14J60"
    ],
    "keywords": [
      "cyclic covers",
      "strong stability",
      "cotangent bundles",
      "absolute frobenius morphism",
      "ample line bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0106L"
    }
  }
}