{
  "id": "math/0112267",
  "version": "v3",
  "published": "2001-12-24T05:59:50.000Z",
  "updated": "2002-09-20T06:49:16.000Z",
  "title": "A note on Fourier-Mukai transform",
  "authors": [
    "Kota Yoshioka"
  ],
  "comment": "19 pages, some results added",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this note, we consider the problem on the preservation of stability under the Fourier-Mukai transforms. We first show that the Fourier-Mukai transform on an abelian surface or a K3 surface does not always preserve the stability, even for a $\\mu$-stable vector bundle. We next provide some positive results on this problem. Finally we discuss the birational map of moduli spaces on an abelian surface.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2002-09-20T06:49:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20"
    ],
    "keywords": [
      "fourier-mukai transform",
      "abelian surface",
      "k3 surface",
      "stable vector bundle",
      "birational map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....12267Y"
    }
  }
}