of importance to find weak coupling solutions, as will be done in the following sections.

The model {#model}
---------

We would like to compactify the type IIB theory on the mirror of a rigid Calabi-Yau manifold [^3]with $h_{11}=0$ and $h_{21}=84$. The theory we are interested in is constructed in terms of a LG model based on nine minimal models and worldsheet superpotential $$\eqlabel{fermat}
W=\sum_{i=1}^9 x_i^3,$$ divided by a ${\zet}_3$ symmetry generated by $$g:x_i \rightarrow \omega x_i,$$ with $i=1,\dots,9$ and $\omega=e^{{2\pi i\over 3}}$. Having $h_{11}=0$ the model has no Kähler moduli (or hypermultiplets except for the universal hypermultiplet) so that it is intrinsically non-geometric.

Constraints following from the tadpole cancellation condition can be satisfied by considering an orientifold of this LG model which can be obtained by dividing by worldsheet parity $\Omega_B$ dressed with a holomorphic involution $P$ in space-time $$P: (x_1,x_2, x_3 \dots x_9)=-(x_2,x_1,x_3,x_4,\dots , x_9).$$ Complex structure deformations emerge as deformations of $W$ and a basis of such deformations is given in terms of the invariant monomials of the chiral ring $$x_ix_jx_k,$$ where $i\neq j\neq k\neq i$. There are $h_{21}=63$ monomials which are invariant under the ${\zet}_3$ action as well as the orientifold action. There are no Kähler structure 