English

Noncommutative resolutions of ADE fibered Calabi-Yau threefolds

Algebraic Geometry 2019-12-09 v3 High Energy Physics - Theory Mathematical Physics math.MP

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".

Keywords

Cite

@article{arxiv.0806.3177,
  title  = {Noncommutative resolutions of ADE fibered Calabi-Yau threefolds},
  author = {Alexander Quintero Velez and Alex Boer},
  journal= {arXiv preprint arXiv:0806.3177},
  year   = {2019}
}

Comments

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