Aspinwall, PS; Morrison, DR, *Quivers from Matrix Factorizations*,
Communications in Mathematical Physics, vol. 313 no. 3
(2012),
pp. 607-633 [arXiv:1005.1042], [doi] .
**Abstract:**

*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 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. © 2012 Springer-Verlag.*