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Abstract: The derived category of bounded complexes of coherent sheaves is one of themost important algebraic invariants of a smooth projective variety. Animportant approach to understand derived categories is to construct fullstrongly exceptional sequences. The problem of characterizing smooth projectivevarieties which have a full strongly exceptional collection and investigatewhether there is one consisting of line bundles is a classical and importantquestion in Algebraic Geometry. Not all smooth projective varieties have a fullstrongly exceptional collection of coherent sheaves. In this paper we give astructure theorem for the derived category of a toric fiber bundle X over Zwith fiber F provided that F and Z have both a full strongly exceptionalcollection of line bundles.

Autor: L. Costa, S. Di Rocco, R.M. Miro-Roig


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