Communications in Mathematical Physics

, Volume 313, Issue 3, pp 607–633 | Cite as

Quivers from Matrix Factorizations

  • Paul S. Aspinwall
  • David R. Morrison


We discuss how matrix factorizations offer a practical method of computing the quiver and associated superpotential for a hypersurface singularity. This method also yields explicit geometrical interpretations of D-branes (i.e., quiver representations) on a resolution given in terms of Grassmannians. As an example we analyze some non-toric singularities which are resolved by a single \({\mathbb{P}^1}\) but have “length” greater than one. These examples have a much richer structure than conifolds. A picture is proposed that relates matrix factorizations in Landau–Ginzburg theories to the way that matrix factorizations are used in this paper to perform noncommutative resolutions.


Matrix Factorization Quiver Gauge Theory Path Algebra Projective Resolution Coherent Sheave 
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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Center for Geometry and Theoretical PhysicsDuke UniversityDurhamUSA
  2. 2.Departments of Mathematics and PhysicsUniversity of CaliforniaSanta BarbaraUSA

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