On decomposition of Bott–Samelson sheaves

Decomposition Numbers for Perverse Sheaves

The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial orbit in a simple Lie algebra. This work has applications to modular representation theory, for Weyl g...

Equivariant Primary Decomposition and Toric Sheaves

We study global primary decompositions in the category of sheaves on a scheme which are equivariant under the action of an algebraic group. We show that equivariant primary decompositions exist if the group is connected. As main application we consider the case of toric sheaves over toric varieties. Comparing these decompositions with primary decompositions of graded and fine graded modules ove...

Sheaves on fibered threefolds and quiver sheaves

This paper classifies a class of holomorphic D-branes, closely related to framed torsion-free sheaves, on threefolds fibered in resolved ADE surfaces over a general curve C, in terms of representations with relations of a twisted Kronheimer– Nakajima-type quiver in the category Coh(C) of coherent sheaves on C. For the local Calabi–Yau case C ∼= A and special choice of framing, one recovers the ...

Sheaves on Algebraic Stacks

Sheaves on Algebraic Stacks