to the complex structures of the three tori, while the remaining moduli correspond to blow up modes.

Here we will focus on stabilizing the bulk moduli and we shall assume that blow up modes have been stabilized at a different scale. This will already give us some useful information about the moduli space. In the next section it is shown how the equations constraining the bulk moduli of the toroidal orbifold of [@wati] emerge as a special case of our equations.

Non-renormalization theorem
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There are several arguments supporting the non-renormalization theorem of the superpotential for complex structure moduli in the type IIB theory. First indirect evidence came from the matrix model calculation of [@DV]. Here we shall elaborate a more direct argument based on supersymmetry that was already presented in [@BVW]. In general, the superpotential of an $\caln=1$ theory receives non-perturbative corrections. However, the particular $\caln=1$ theory we are interested in has its origin in a theory with $\caln=2$ supersymmetry, so that corrections to the superpotential are absent.

Compactifying the type IIB theory on a Calabi-Yau threefold will in general result in a theory with $\caln=2$ supersymmetry in $d=4$ containing $h^{21}$ vector multiplets and $h^{11}+1$ hypermultiplets (where the ‘1’ 