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Noncommutative Resolutions of ADE Fibered Calabi-Yau Threefolds

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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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Authors and Affiliations

  1. Mathematics Department, University of Glasgow, University Gardens, Glasgow, G12 8QW, UK

    Alexander Quintero Vélez

  2. Mathematisch Instituut, Universiteit Utrecht, P. O. Box 80010, 3508 TA, Utrecht, The Netherlands

    Alexander Quintero Vélez & Alex Boer

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  1. Alexander Quintero Vélez
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  2. Alex Boer
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Correspondence to Alexander Quintero Vélez.

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Communicated by A. Connes

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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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