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. http://arxiv.org/abs/hep-th/0108120v2, 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. http://arxiv.org/abs/math/0612139v2, 2006) which we call the “N = 1 ADE quiver algebra”.
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Quintero Vélez, A., Boer, A. Noncommutative Resolutions of ADE Fibered Calabi-Yau Threefolds. Commun. Math. Phys. 297, 597–619 (2010). https://doi.org/10.1007/s00220-010-1052-5
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DOI: https://doi.org/10.1007/s00220-010-1052-5