imply that it can be expressed in terms of $\mathcal{I}$, see e.g. Ref. [@Meessen:2006tu] or Eq. (\[eq:MRI\]).

Eqs. (\[eq:stabilization\]) are sometimes known as the *generalized stabilization equations*, the standard stabilization equations having the same form but with the harmonic functions $(\mathcal{I}^{\Lambda},\mathcal{I}_{\Lambda})$ replaced by magnetic and electric charges, [*e.g.*]{} $(p^{\Lambda},q_{\Lambda})$.

The real part of $\mathcal{V}/X$, denoted by $\mathcal{R}\equiv
(\mathcal{R}^{\Lambda},\mathcal{R}_{\Lambda})$ can, in principle, be written in terms of the real harmonic functions, which is usually referred to as “solving the stabilization equations”. In theories with a prepotential, the homogeneity properties of the prepotential allow us to write

$$\label{eq:MdF}
  \mathcal{M}_{\Lambda}/X =
\frac{\partial \mathcal{F}(\mathcal{L}^{\cdot}/X)}{\partial (\mathcal{L}^{\Lambda}/X)}\, .$$

Taking the imaginary part of this equation, we have

$$\label{eq:IRHH}
\mathcal{I}_{\Lambda} (\mathcal{R}^{\cdot},\mathcal{I}^{\cdot})
=\mathcal{I}_{\Lambda}\, ,$$

which implicitly defines $\mathcal{R}^{\Lambda}(\mathcal{I}^{\cdot},\mathcal{I}_{\cdot})$, although solving these equations can be extremely hard and in general the explicit solution is unknown.

The real part of Eqs. (\[eq:MdF\]) and the above solutions give straightforwardly the functions $R_{\Lambda}(R^{\cdot}(\mathcal{I}^{\cdot},\mathcal{I}_{\cdot}),
\mathcal{I}^{\cdot})$.

Having the complete symplectic section $\mathcal{V}/X$ entirely given in terms of the real harmonic functions, one can construct the fields of the solutions as follows:

1.  The $n$ complex scalar fields $Z^{i}$ are given by the quotients

    $$\label{eq:scalars}
       Z^{i}= \frac{\mathcal{L}^{i}/X}{\mathcal{L}^{0}/X}=
    \frac{\mathcal{R}^{i}+i\mathcal{I}^{i}}{\mathcal{R}^{0}+i\mathcal{I}^{0}}\, .$$

2.  The metric has the form

    