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Noncommutative Resolutions of ADE Fibered Calabi-Yau Threefolds
Authors:Alexander Quintero Vélez  Alex Boer
Affiliation:1. Mathematics Department, University of Glasgow, University Gardens, Glasgow, G12 8QW, UK
2. Mathematisch Instituut, Universiteit Utrecht, P. O. Box 80010, 3508 TA, Utrecht, The Netherlands
Abstract:In this paper we construct noncommutative resolutions of a certain class of Calabi-Yau threefolds studied by Cachazo et al. (Geometric transitions and N = 1 quiver theories. , 2001). 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 Ginzburg (Calabi-Yau algebras. , 2006) which we call the “N = 1 ADE quiver algebra”.
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