{
  "id": "math/0506429",
  "version": "v1",
  "published": "2005-06-21T12:26:33.000Z",
  "updated": "2005-06-21T12:26:33.000Z",
  "title": "Derived categories of coherent sheaves on rational homogeneous manifolds",
  "authors": [
    "Christian Böhning"
  ],
  "comment": "82 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Starting point of the present work is a conjecture of F. Catanese which says that in the derived category of coherent sheaves on any rational homogeneous manifold G/P there should exist a complete strong exceptional poset and a bijection of the elements of the poset with the Schubert varieties in G/P such that the partial order on the poset is the order induced by the Bruhat-Chevalley order. The goal of this work is to provide further evidence for Catanese's conjecture, clarify some aspects of it and supply new techniques. In particular we prove a theorem on the derived categories of quadric bundles, and show how one can find \"small\" generating sets for D^b(X) on symplectic or orthogonal isotropic Grassmannians by fibrational techniques.- The last section discusses a different approach based on a theorem of M. Brion and cellular resolutions of monomial ideals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-06-21T12:26:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05",
      "14M15",
      "18E30"
    ],
    "keywords": [
      "derived category",
      "coherent sheaves",
      "complete strong exceptional poset",
      "rational homogeneous manifold g/p",
      "orthogonal isotropic grassmannians"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 82,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6429B"
    }
  }
}