Derived categories of coherent sheaves on rational homogeneous manifolds

Details Derived categories of coherent sheaves on rational homogeneous manifolds Derived categories of coherent sheaves on rational homogeneous manifolds

2005-06-21

arxiv.org/abs/math/0506429v1

Mathematics

Algebraic Geometry

82 pages

Scientific paper

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.

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