Sheaves on fibered threefolds and quiver sheaves
Abstract
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 C1 and special choice of framing, one recovers the N=1 ADE quiver studied by Cachazo--Katz--Vafa.
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