  We analyze the locus, together with multiplicities, of "bad" conformal field
theories in the compactified moduli space of N=(2,2) superconformal field
theories in the context of the generalization of the Batyrev mirror
construction using the gauged linear sigma-model. We find this discriminant of
singular theories is described beautifully by the GKZ "A-determinant" but only
if we use a noncompact toric Calabi-Yau variety on the A-model side and
logarithmic coordinates on the B-model side. The two are related by "local"
mirror symmetry. The corresponding statement for the compact case requires
changing multiplicities in the GKZ determinant. We then describe a natural
structure for monodromies around components of this discriminant in terms of
spherical functors. This can be considered a categorification of the GKZ
A-determinant. Each component of the discriminant is naturally associated with
a category of massless D-branes.

High Energy Physics - Theory;Algebraic Geometry