  We clarify certain important issues relevant for the geometric interpretation
of a large class of N = 2 superconformal theories. By fully exploiting the
phase structure of these theories (discovered in earlier works) we are able to
clearly identify their geometric content. One application is to present a
simple and natural resolution to the question of what constitutes the mirror of
a rigid Calabi-Yau manifold. We also discuss some other models with unusual
phase diagrams that highlight some subtle features regarding the geometric
content of conformal theories.
