Noncommutative resolutions of ADE fibered Calabi-Yau threefolds
arXiv:0806.3177 · doi:10.1007/s00220-010-1052-5
Abstract
In this paper we construct noncommutative resolutions of a certain class of Calabi-Yau threefolds studied by F. Cachazo, S. Katz and C. Vafa. The threefolds under consideration are fibered over a complex plane with the fibers being deformed Kleinian singularities. The construction is in terms of a noncommutative algebra introduced by V. Ginzburg, which we call the "N=1 ADE quiver algebra".
20 pages; v3: published version -all preliminary material has been removed; Subsect. 3.1 has been rewritten and expanded and it is now presented as Sect. 1 in an attempt to translate many of the undefined terms in the physics literature in a precise way