a four-dimensional Minkowski space are obtained as solutions of $$\eqlabel{minkow1} W=D_\tau W=D_t W=0,$$ which can equivalently be written as $$\eqlabel{minkow2} W_{RR}=W_{NS}=0\qquad {\rm and } \qquad \tau =
{W'_{RR}(t)\over W'_{NS}(t)}.$$ We are interested in finding physical solutions for which the imaginary parts of $t$ and $\tau$ are non-vanishing, because otherwise the solutions lie at the boundary of the moduli space. Since vanishing of the superpotentials results in cubic equations with real coefficients, complex solutions of these equations only exist if the cubic polynomials $W_{RR}$ and $W_{NS}$ have two common complex conjugate roots, [*i.e.*]{} if they factorize according to $$\begin{split}
W_{RR}& =C(t-\alpha)(t-a)(t-\bar a), \\
W_{NS}&= D(t-\beta)(t-a)(t-\bar a), \\
\end{split}$$ where $C,D,\alpha,\beta$ are real and $a$ is complex. These numbers are constrained by flux quantization condition. The complex structure is then determined from the zeros of a quadratic equation, or equivalently $$\eqlabel{quads}
t = a=a_1+i a_2.$$ Moreover, taking into account Eqs. (\[basis\]), (\[fluxes\]), (\[minkow1\]), (\[minkow2\]) the tadpole can be written in the form $$\eqlabel{tads} \int H_{RR} \wedge H_{NS}=4(M_2 N_0-N_2 M_0) (a_2)^2.$$ Note that the coefficient in front of $(a_2)^2$ is integer and cannot be made arbitrarily small nor equal to zero (the lhs of the equation does never vanish in Minkowski). As a 