  We consider the compactification of the IIA string to (1+1) dimensions on
non-compact 4-folds that are ALE fibrations. Supersymmetry requires that the
compactification include 4-form fluxes, and a particular class of these models
has been argued by Gukov, Vafa and Witten to give rise to a set of perturbed
superconformal coset models that also have a Landau-Ginzburg description. We
examine all these ADE models in detail, including the exceptional cosets. We
identify which perturbations are induced by the deformation of the singularity,
and compute the Landau-Ginzburg potentials exactly. We also show how the the
Landau-Ginzburg fields and their superpotentials arise from the geometric data
of the singularity, and we find that this is most naturally described in terms
of non-compact, holomorphic 4-cycles.
