Possible Phase Transitions among Calabi-Yau Compactifications

We study a wide class of complex spaces each of which may be spanned by "internal" degrees of freedom of certain physics models with simple supergravity in (3+1)-dimensional Minkowski space-time. We show that there are connections among these complex spaces suggesting the possibility of phase transitions which would cause drastic changes in the physical observables of such models. The web of superstring models so connected suggests the existence of a "unified" superstring model of which the models studied here are special cases.