  We study moduli space stabilization of a class of BPS configurations from the
perspective of the real intrinsic Riemannian geometry. Our analysis exhibits a
set of implications towards the stability of the D-term potentials, defined for
a set of abelian scalar fields. In particular, we show that the nature of
marginal and threshold walls of stabilities may be investigated by real
geometric methods. Interestingly, we find that the leading order contributions
may easily be accomplished by translations of the Fayet parameter.
Specifically, we notice that the various possible linear, planar, hyper-planar
and the entire moduli space stabilities may easily be reduced to certain
polynomials in the Fayet parameter. For a set of finitely many real scalar
fields, it may be further inferred that the intrinsic scalar curvature defines
the global nature and range of vacuum correlations. Whereas, the underlying
moduli space configuration corresponds to a non-interacting basis at the zeros
of the scalar curvature, where the scalar fields become un-correlated. The
divergences of the scalar curvature provide possible phase structures, viz.,
wall of stability, phase transition, if any, in the chosen moduli
configuration. The present analysis opens up a new avenue towards the
stabilizations of gauge and string moduli.
