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Mathematics > Algebraic Geometry

arXiv:0908.0846 (math)
[Submitted on 6 Aug 2009 (v1), last revised 18 Oct 2010 (this version, v2)]

Title:Derived category of toric fibrations

Authors: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.
Comments: The main result of this paper proves the final conjecture that generalizes the results contained in arXiv:0908.0846
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14F05
Cite as: arXiv:0908.0846 [math.AG]
  (or arXiv:0908.0846v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.0908.0846

Submission history

From: Sandra Di Rocco [view email]
[v1] Thu, 6 Aug 2009 11:41:16 UTC (13 KB)
[v2] Mon, 18 Oct 2010 11:44:49 UTC (25 KB)
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