On Phases of Generic Toric Singularities

We systematically study the phases of generic toric singularities, using methods initiated in hep-th/0612046. These correspond to Gauged Linear Sigma Models with arbitrary charges. We show that complete information about generic $U(1)^r$ GLSMs can be obtained by studying the GLSM Lagrangian, appropriately modified in the different phases of the theory. This can be used to study the different phases of $L^{a,b,c}$ spaces and their non-supersymmetric counterparts.