Mathematics – Algebraic Geometry
Scientific paper
2009-08-06
Mathematics
Algebraic Geometry
The main result of this paper proves the final conjecture that generalizes the results contained in arXiv:0908.0846
Scientific paper
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.
Costa Laura
Miró-Roig Rosa María
Rocco Sandra Di
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