L. Costa, S. Di Rocco, R. M. Miro-Roig
Published 2009-08-06, updated 2010-10-18Version 2
The derived category of bounded complexes of coherent sheaves is one of the most important algebraic invariants of a smooth projective variety. An important approach to understand derived categories is to construct full strongly exceptional sequences. The problem of characterizing smooth projective varieties which have a full strongly exceptional collection and investigate whether there is one consisting of line bundles is a classical and important question in Algebraic Geometry. Not all smooth projective varieties have a full strongly exceptional collection of coherent sheaves. In this paper we give a structure theorem for the derived category of a toric fiber bundle X over Z with fiber F provided that F and Z have both a full strongly exceptional collection of line bundles.
Comments: The main result of this paper proves the final conjecture that generalizes the results contained in arXiv:0908.0846
Frobenius splitting and Derived category of toric varieties
On the derived category of $\bar{M}_{0,n}$
Derived categories of coherent sheaves on rational homogeneous manifolds
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