ON THE GEOMETRIC INTERPRETATION OF N=2 SUPERCONFORMAL THEORIES

We clarify certain important issues relevant for the geometric interpr etation of a large class of N = 2 superconformal theories. By fully ex ploiting the phase structure of these theories (discovered in earlier works) we are able to clearly identify their geometric content. One ap plication is to present a simple and natural resolution to the questio n of what constitutes the mirror of a rigid Calabi-Yau manifold. We al so discuss some other models with unusual phase diagrams that highligh t some subtle features regarding the geometric content of conformal th eories.