{
  "id": "1411.1799",
  "version": "v1",
  "published": "2014-11-07T00:04:17.000Z",
  "updated": "2014-11-07T00:04:17.000Z",
  "title": "Derived categories of cyclic covers and their branch divisors",
  "authors": [
    "Alexander Kuznetsov",
    "Alexander Perry"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, we consider a degree $n$ cyclic cover $X \\to Y$ ramified over a divisor $Z \\subset Y$. We construct semiorthogonal decompositions of $\\mathrm{D^b}(X)$ and $\\mathrm{D^b}(Z)$ with distinguished components $\\mathcal{A}_X$ and $\\mathcal{A}_Z$, and prove the equivariant category of $\\mathcal{A}_X$ (with respect to an action of the $n$-th roots of unity) admits a semiorthogonal decomposition into $n-1$ copies of $\\mathcal{A}_Z$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-07T00:04:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic cover",
      "derived category",
      "branch divisors",
      "rectangular lefschetz decomposition",
      "construct semiorthogonal decompositions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1799K"
    }
  }
}