{
  "id": "math/0608127",
  "version": "v4",
  "published": "2006-08-04T17:23:43.000Z",
  "updated": "2009-11-18T20:08:20.000Z",
  "title": "GV-sheaves, Fourier-Mukai transform, and Generic Vanishing",
  "authors": [
    "Giuseppe Pareschi",
    "Mihnea Popa"
  ],
  "comment": "28 pages; many more corrections and improved statements with respect to previous versions; especially fixed some inaccuracies pointed out by the referees when working with singular varieties,and extended the general results to the Cohen-Macaulay case. Final version, to appear in Amer. J.Math",
  "categories": [
    "math.AG"
  ],
  "abstract": "We use homological methods to establish a formal criterion for Generic Vanishing, in the sense originated by Green and Lazarsfeld and pursued further by Hacon and the first author, but in the context of an arbitrary Fourier-Mukai correspondence. For smooth projective varieties we apply this to deduce a Kodaira-type generic vanishing theorem for adjoint bundles of the form $K_X + L$ with $L$ a nef line bundle, and in fact a more general generic Nadel-type vanishing theorem for multiplier ideal sheaves. Still in the context of the Picard variety, the same method generates various other generic vanishing results, by reduction to standard vanishing theorems. We further use the formal criterion in order to address examples related to generic vanishing on higher rank moduli spaces (on curves and on some threefold Calabi-Yau fiber spaces).",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-11-18T20:08:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F17",
      "14F05"
    ],
    "keywords": [
      "fourier-mukai transform",
      "general generic nadel-type vanishing theorem",
      "formal criterion",
      "gv-sheaves",
      "threefold calabi-yau fiber spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8127P"
    }
  }
}