  Because of the existence of rigid Calabi--Yau manifolds, mirror symmetry
cannot be understood as an operation on the space of manifolds with vanishing
first Chern class. In this article I continue to investigate a particular type
of K\"ahler manifolds with positive first Chern class which generalize
Calabi--Yau manifolds in a natural way and which provide a framework for
mirrors of rigid string vacua. This class is comprised of a special type of
Fano manifolds which encode crucial information about ground states of the
superstring. It is shown in particular that the massless spectra of
$(2,2)$--supersymmetric vacua of central charge $\hat{c}=D_{crit}$ can be
derived from special Fano varieties of complex dimension $(D_{crit}+2(Q-1))$,
$Q>1$, and that in certain circumstances it is even possible to embed
Calabi--Yau manifolds into such higher dimensional spaces. The constructions
described here lead to new insight into the relation between exactly solvable
models and their mean field theories on the one hand and their corresponding
Calabi--Yau manifolds on the other. It is furthermore shown that Witten's
formulation of the Landau--Ginzburg/Calabi--Yau relation can be applied to the
present framework as well.
