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

2006/12/27 by Samokhin, Alexander
#14M15 #18E30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0612800

Abstract

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.

Related

• Derived categories of coherent sheaves
• Derived categories of coherent sheaves on rational homogeneous manifolds
• Derived categories of coherent sheaves on abelian varieties and equivalences between them
• Semiorthogonal decompositions of the categories of equivariant coherent\n sheaves for some reflection groups
• Semiorthogonal decomposition for algebraic varieties