Some remarks on the derived categories of coherent sheaves on homogeneous spaces

Details Some remarks on the derived categories of coherent sheaves on homogeneous spaces Some remarks on the derived categories of coherent sheaves on homogeneous spaces

2006-12-27

arxiv.org/abs/math/0612800v1

Mathematics

Algebraic Geometry

Final version. 14 pages, to appear in Journal Lond. Math. Soc

Scientific paper

In this paper we prove first a general theorem on semiorthogonal decompositions in derived categories of coherent sheaves for flat families over a smooth base. Based on the results of math.AG/0510670, we then show that the derived categories of coherent sheaves on flag varieties of classical type are generated by complete exceptional collections. Finally, we find complete exceptional collections in the derived categories of some homogeneous spaces of the symplectic groups of small rank.

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