Phases of mirror symmetry

Abstract

We review the geometrical framework required for understanding the moduli space of $(2,2)$ superconformal-field theories, highlighting various aspects of its phase structure. In particular, we indicate the types of phase diagrams that emerge for ``generic'' Calabi-Yau theories and review an efficient method for their determination. We then focus on some special types of phase diagrams that have bearing on the issues of rigid manifolds, mirror symmetry and geometrical duality.