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arXiv · 0908.0846

Derived category of toric fibrations

L. Costa·S. Di Rocco·R. M. Miro-Roig
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Abstract

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.

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L. Costa, S. Di Rocco, R. M. Miro-Roig. 2009-08-06. Derived category of toric fibrations. https://arxiv.org/abs/0908.0846

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